Academic literature on the topic 'Proper coloring'
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Journal articles on the topic "Proper coloring"
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Ma, Baolin, and Chao Yang. "Distinguishing colorings of graphs and their subgraphs." AIMS Mathematics 8, no. 11 (2023): 26561–73. http://dx.doi.org/10.3934/math.20231357.
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<abstract><p>In this paper, several distinguishing colorings of graphs are studied, such as vertex distinguishing proper edge coloring, adjacent vertex distinguishing proper edge coloring, vertex distinguishing proper total coloring, adjacent vertex distinguishing proper total coloring. Finally, some related chromatic numbers are determined, especially the comparison of the correlation chromatic numbers between the original graph and the subgraphs are obtained.</p></abstract>
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Goddard, Wayne, and Robert Melville. "Coloring subgraphs with restricted amounts of hues." Open Mathematics 15, no. 1 (September 22, 2017): 1171–80. http://dx.doi.org/10.1515/math-2017-0098.
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Abstract We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we consider (not necessarily proper) colorings of the vertices of a graph G such that, for every copy of F in G, the number of colors it receives is in A. This generalizes proper colorings, defective coloring, and no-rainbow coloring, inter alia. In this paper we focus on the case that A is a singleton set. In particular, we investigate the colorings where the graph F is a star or is 1-regular.
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Chartrand, Gary, James Hallas, and Ping Zhang. "Royal Colorings of Graphs." Ars Combinatoria 156 (July 31, 2023): 51–63. http://dx.doi.org/10.61091/ars156-06.
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For a graph \(G\) and a positive integer \(k\), a royal \(k\)-edge coloring of \(G\) is an assignment of nonempty subsets of the set \(\{1, 2, \ldots, k\}\) to the edges of \(G\) that gives rise to a proper vertex coloring in which the color assigned to each vertex \(v\) is the union of the sets of colors of the edges incident with \(v\). If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal \(k\)-coloring. The minimum positive integer \(k\) for which a graph has a strong royal \(k\)-coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.
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Chartrand, Gary, James Hallas, and Ping Zhang. "Royal Colorings of Graphs." Ars Combinatoria 156 (July 31, 2023): 51–63. http://dx.doi.org/10.61091/ars156-6.
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For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v . If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal k coloring. The minimum positive integer k for which a graph has a strong royal k -coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of trees.
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Keszegh, Balázs, and Dömötör Pálvölgyi. "Proper Coloring of Geometric Hypergraphs." Discrete & Computational Geometry 62, no. 3 (May 15, 2019): 674–89. http://dx.doi.org/10.1007/s00454-019-00096-9.
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Bagheri Gh., Behrooz, and Behnaz Omoomi. "On the simultaneous edge coloring of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (October 10, 2014): 1450049. http://dx.doi.org/10.1142/s1793830914500499.
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A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et al. (2000) conjectured that every bridgeless bipartite graph is 2-simultaneous edge colorable. Luo et al. (2004) showed that every bipartite graphic sequence S with all its elements greater than one, has a realization that admits a 2-simultaneous edge coloring. In this paper, the μ-simultaneous edge coloring of graphs is studied. Moreover, the properties of the extremal counterexample to the above conjecture are investigated. Also, a relation between 2-simultaneous edge coloring of a graph and a cycle double cover with certain properties is shown and using this relation, some results about 2-simultaneous edge colorable graphs are obtained.
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Zhou, Yangyang, Dongyang Zhao, Mingyuan Ma, and Jin Xu. "Domination Coloring of Graphs." Mathematics 10, no. 6 (March 21, 2022): 998. http://dx.doi.org/10.3390/math10060998.
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A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by χdd(G). In this paper, we study the complexity of the k-domination coloring problem by proving its NP-completeness for arbitrary graphs. We give basic results and properties of χdd(G), including the bounds and characterization results, and further research χdd(G) of some special classes of graphs, such as the split graphs, the generalized Petersen graphs, corona products, and edge corona products. Several results on graphs with χdd(G)=χ(G) are presented. Moreover, an application of domination colorings in social networks is proposed.
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Li, Minhui, Shumin Zhang, Caiyun Wang, and Chengfu Ye. "The Dominator Edge Coloring of Graphs." Mathematical Problems in Engineering 2021 (October 7, 2021): 1–7. http://dx.doi.org/10.1155/2021/8178992.
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Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .
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Kristiana, Arika Indah, Ahmad Aji, Edy Wihardjo, and Deddy Setiawan. "on Graceful Chromatic Number of Vertex amalgamation of Tree Graph Family." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 3 (October 11, 2022): 432–44. http://dx.doi.org/10.18860/ca.v7i3.16334.
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Proper vertex coloring c of a graph G is a graceful coloring if c is a graceful k-coloring for k∈{1,2,3,…}. Definition graceful k-coloring of a graph G=(V,E) is a proper vertex coloring c:V(G)→{1,2,…,k);k≥2, which induces a proper edge coloring c':E(G)→{1,2,…,k-1} defined c'(uv)=|c(u)-c(v)|. The minimum vertex coloring from graph G can be colored with graceful coloring called a graceful chromatic number with notation χg (G). In this paper, we will investigate the graceful chromatic number of vertex amalgamation of tree graph family with some graph is path graph, centipede graph, broom and E graph.
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Sagan, Bruce, and Vincent Vatter. "Bijective Proofs of Proper Coloring Theorems." American Mathematical Monthly 128, no. 6 (May 28, 2021): 483–99. http://dx.doi.org/10.1080/00029890.2021.1901460.
Full textDissertations / Theses on the topic "Proper coloring"
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Borozan, Valentin. "Proper and weak-proper trees in edges-colored graphs and multigraphs." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00738959.
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Dans la présente thèse nous étudions l'extraction d'arbres dans des graphes arêtes-coloriés.Nous nous concentrons sur la recherche d'arbres couvrants proprement arête-coloriés et faiblement arête-coloriés, notée PST et WST. Nous montrons que les versions d'optimisation de ces problèmes sont NP-Complete dans le cas général des graphes arêtes-coloriés, et nous proposons des algorithmes pour trouver ces arbres dans le cas des graphes arêtes-coloriés sans cycles proprement arêtes-coloriés.Nous donnons également quelques limites de nonapproximabilité. Nous proposons des conditions suffisantes pour l'existence de la PST dans des graphes arêtes-coloriés (pas forcément propre), en fonction de différents paramètres de graphes, tels que : nombre total de couleurs, la connectivité et le nombre d'arêtes incidentes dedifférentes couleurs pour un sommet. Nous nous intéressons aux chemins hamiltoniens proprement arêtes-coloriés dans le casdes multigraphes arêtes-coloriés. Ils présentent de l'intérêt pour notre étude, car ce sontégalement des arbres couvrants proprement arêtes-coloriés. Nous établissons des conditions suffisantes pour qu'un multigraphe contienne un chemin hamiltonien proprement arêtes-coloriés, en fonction de plusieurs paramètres tels que le nombre d'arêtes, le degré d'arêtes, etc. Puisque l'une des conditions suffisantes pour l'existence des arbres couvrants proprement arêtes-coloriés est la connectivité, nous prouvons plusieurs bornes supérieures pour le plus petit nombre de couleurs nécessaires pour la k-connectivité-propre. Nous énonçons plusieurs conjectures pour les graphes généraux et bipartis, et on arrive à les prouver pour k = 1.
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Rodríguez, Porras Cristóbal. "Une analyse ensembliste des opérateurs sur l'espace de Banach l_infty/c-0." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC258.
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On étudie des opérateurs linéaires et continus sur l'espace X=l_infty/c_O et des espaces liés. On commence par examiner des opérateurs T:X → X. On s'intéresse à la possibilité de représenter ses fragments de la forme T_{B,A}:l_infty(A)/c_0(A)→, l_infty(B)/c_0(B), pour A,B C̱ N infinis, par des applications de l_infty(A) dans l_infty(B), des matrices AxB, des fonctions continues de B^*=βB\B dans A^ *, ou des bijections de B dans A. On montre plusieurs exemples. On définit et on étudie de nouvelles classes d'opérateurs. Pour certaines d'entre elles on obtient des représentations satisfactoires. Pour d'autres classes, on montre que c'est impossible. On montre des automorphismes de X qui ne se relèvent pas à des opérateurs sur l_infty et on montre que sous OCA+MA tout automorphisme sans fontaines ou sans entonnoirs est induit par une bijection localement (au sens qu'on vient de spécifier). Cet axiome supplémentaire est nécessaire, comme témoignent des contre-exemples de plusieurs types construits avec HC. Ensuite, on regarde les plongements isomorphiques de l_infty(X) dans X. On démontre que sous PFA la structure locale des opérateurs de chaque coordonnée a une grande influence sur l'opérateur original, ce qui entraîne l'impossibilité de plonger l_infty(X) dans X sous PFA par des opérateurs dans plusieurs classes bien connues. Cela contraste avec la construction de Drewnowski et Roberts d'un tel plongement sous HC comme opérateur de composition. Finalement, on présente une démonstration moderne d'une version améliorée d'un résultat de Kadec et Pelczyński sur des séquences de mesures de Radon. On montre des applications de ce résultat aux opérateurs sur XWe investigate linear bounded operators on X=l_infty/c_O and related spaces. We begin by studying operators T:X→X focusing on the possibility of representing their fragments of the form T_{B,A}:l_infty(A)/c_0(A)→, l_infty(B)/c_0(B) for A,BCN infinite by means of operators from Linfty(A) into l_infty(B), infinite AxB-matrices, continuous maps from B^*=βB\B into A^*, or bijections from B to A. We present many examples, introduce and investigate several classes of operators; for some we obtain satisfactory representations and for others we show that it is impossible. We show that there are automorphisms of X which cannot be lifted to operators on l_infty and assuming OCA+MA we show that every automorphism of X with no fountains or with no funnels is locally, i. E. , for some infinite A,B C̱N as above, induced by a bijection from B to A. This additional set-theoretic assumption is necessary as we show that the Continuum Hypothesis implies the existence of counterexamples of diverse flavours. Later, we look into isomorphic embeddings of the l_infty-sum of X into X. We show that under PFA the localstructure of the induced coordinate operators has great influence over the original operator. As an application, we show the impossibility under PFA of embedding Linfty(X) into X by means of some well-known classes of operators, contrasting with Drewnowski and Roberts' construction under CH of such an embedding as a composition operator. Finally, we present a modem proof of a slightly improved version of a result by Kadec and Pelczyński on sequences of Radon measures. We show an application of this resuit to operators from X into itself
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Ouyang, Qiancheng. "Some colouring problems in edge/vertex-coloured graphs : Structural and extremal studies." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPASG060.
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La coloration de graphes est l'un des sujets les plus connus, populaires et largement étudiés dans le domaine de la théorie des graphes, avec une vaste littérature comprenant des approches provenant de nombreux domaines ainsi que de nombreux problèmes qui sont encore ouverts et étudiés par divers mathématiciens et informaticiens à travers le monde. Le Problème des Quatre Couleurs, à l'origine de l'étude de la coloration des graphes, a été l'un des problèmes centraux en théorie des graphes au siècle dernier. Il demande s'il est possible de colorer proprement chaque graphe planaire avec quatre couleurs. Malgré son origine théorique, la coloration des graphes a trouvé de nombreuses applications pratiques telles que la planification, les problèmes d'assignation de fréquences, la segmentation, etc. Le Problème des Quatre Couleurs est l'un des problèmes importants parmi de nombreux problèmes de la théorie des graphes chromatiques, à partir duquel de nombreuses variantes et généralisations ont été proposées. Tout d'abord, dans cette thèse, nous visons à optimiser la stratégie de coloration des sommets de graphes et d'hypergraphes avec certaines contraintes données, en combinant le concept de coloration propre et d'élément représentatif de certains sous-ensembles de sommets. D'autre part, en fonction du sujet à colorer, une grande quantité de recherches et de problèmes de graphes à arêtes colorées ont émergé, avec des applications importantes en biologie et en technologies web. Nous fournissons quelques résultats analogues pour certaines questions de connectivité, afin de décrire des graphes dont les arêtes sont attribuées suffisamment de couleurs, garantissant ainsi des arbres couvrants ou des cycles ayant une structure chromatique spécifiqueGraph colouring is one of the best known, popular and extensively researched subject in the field of graph theory, having a wide literature with approaches from many domains and a lot of problems, which are still open and studied by various mathematicians and computer scientists along the world. The Four Colour Problem, originating the study of graph colouring, was one of the central problem in graph theory in the last century, which asks if it is possible to colour every planar graph properly by four colours. Despite the theoretical origin, the graph colouring has found many applications in practice like scheduling, frequency assignment problems, segmentation, etc. The Four Colour Problem is a significant one among many problems in chromatic graph theory, from which many variants and generalizations have been proposed. Firstly, in this thesis, we aim to optimize the strategy to colour the vertex of graphs and hypergraphs with some given constraints, which combines the concept of proper colouring and representative element of some vertex subsets. On the other hand, according to the subject to be coloured, a large amount of research and problems of edge-coloured graphs have emerged, which have important applications to biology and web technologies. We provide some analogous results for some connectivity issues—to describe graphs whose edges are assigned enough colours, that guarantee spanning trees or cycles of a specific chromatic structure
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Cairncross, Emily. "Proper 3-colorings of cycles and hypercubes." Oberlin College Honors Theses / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1621606265779497.
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Mendy, Gervais. "Chaînes alternées dans les graphes arête-coloriés : k-linkage et arbres couvrants." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00769929.
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Un graphe arête-colorié Gc est un graphe dont les arêtes sont coloriées par un ensemble de couleurs données. Un sous-graphe de Gc est dit proprement colorié s'il ne contient pas d'arêtes adjacentes de même couleur. Un graphe ou multigraphe c-arête-colorié Gc, est dit k-lié (respectivement k-arête-lié) si et seulement si quelque soient 2k sommets distincts de V(Gc), notés, x1 y1 , x2 y2 , ..., xk yk , il existe k chaînes élémentaires sommet-disjointes (respectivement arête-disjointes) proprement arête-coloriées, reliant x1 à y1 , x2 à y2 , ... , xk à yk .Un arbre couvrant propre d'un graphe Gc est un sous-graphe de Gc qui est un arbre couvrant proprement colorié.Un arbre couvrant faiblement colorié est une arborescence telle qu'il existe une chaîne proprement coloriée entre la racine et chaque sommet du graphe.Dans la première partie de cette thèse, nous donnons des conditions suffisantes pour qu'un graphe arête-colorié soit k-lié. C'est un problème classique en théorie des graphes, avec des applications multiples. Ainsi, nous avons établi entre autres les résultats suivants.A) Tout multigraphe 2-arête-colorié d'ordre n ≥ 242k tel que dc(Gc) ≥ n/2+k -1, est k-lié. B) Tout multigraphe c-arête-colorié d'ordre n ≥ 2k et de taille m≥ cn(n-1)/2 - c(n-2k +1)+1 est k-lié.C) Tout multigraphe c-arête-colorié d'ordre n ≥ 2k tel que dc(x) ≥ n/2 pour tout sommet x, est k-arête-lié.D) Tout multigraphe 2-arête-colorié d'ordre n ≥ 2k ≥ 10 et de taille m ≥ n2 -5n + 11 tel que dc(x) ≥ 1 pour tout sommet x, est k-arête-lié.Dans la seconde partie de cette thèse, deux autres problèmes classiques en théorie des graphes sont traités dans la version arête-coloriée. Il s'agit des arbres couvrants et des chaînes hamiltoniennes. Nous donnons ci-dessous quelques résultats.E) Tout graphe simple c-arête-colorié k-connexe d'ordre n ≥ C²k+1 + k + 2 avec c ≥ C²n-k-1 + k +1, a un arbre couvrant propre.F) Tout graphe Gc connexe c-arête-colorié de degré rainbow rd(Gc)=k et d'ordre n ≥ C²k+1 + k + 2 avec c ≥ C²n-k-1 + k +1, possède un arbre couvrant propre.G) Tout graphe simple c-arête-colorié k-connexe d'ordre n ≥ ((k + j)2 + 3(k + j) - 2)/2 avec c ≥ ((n - k - j)(n - k - j - 1))/2 + 2 , où j(j -1)=k , possède un arbre couvrant faiblement colorié.H) Tout multigraphe Gc d'ordre n ≥ 14 et de taille m ≥ (n - 3)(n - 4) + 3n - 2 tel que rd(Gc) = 2, possède une chaîne hamiltonienne propre. I) Tout multigraphe c-arête-colorié d'ordre n ≠ 5, 7 et de taille m ≥ n2 - 3n + 4, possède une chaîne hamiltonienne propre.La plupart des résultats exposés, sont les meilleurs possibles relativement aux propriétés sur les conditions suffisantes.
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Montero, Leandro Pedro. "Graphes et couleurs : graphes arêtes-coloriés, coloration d'arêtes et connexité propre." Phd thesis, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00776899.
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Dans cette thèse nous étudions différents problèmes de graphes et multigraphes arêtes-coloriés tels que la connexité propre, la coloration forte d'arêtes et les chaînes et cycles hamiltoniens propres. Enfin, nous améliorons l'algorithme connu $O(n^4)$ pour décider du comportement d'un graphe sous opérateur biclique, en étudiant les bicliques dans les graphes sans faux jumeaux. Plus précisément, 1) Nous étudions d'abord le nombre $k$-connexité-propre des graphes, noté $pc_k(G)$, ç'est à dire le nombre minimum de couleurs nécessaires pour colorer les arêtes d'un graphe de façon à ce qu'entre chaque paire de sommets, ils existent $k$ chemins intérieurement sommet-disjoints. Nous prouvons plusieurs bornes supérieures pour $pc_k(G)$. Nous énonçons quelques conjectures pour les graphes généraux et bipartis et nous les prouvons dans le cas où $k = 1$. 2) Nous étudions l'existence de chaînes et de cycles hamiltoniens propres dans les multigraphes arêtes-coloriés. Nous établissons des conditions suffisantes, en fonction de plusieurs paramètres tels que le nombre d'arêtes, le degré arc-en-ciel, la connexité, etc. 3) Nous montrons que l'indice chromatique fort est linéaire au degré maximum pour tout graphe $k$-dégénéré où, $k$ est fixe. En corollaire, notre résultat conduit à une amélioration des constantes et donne également un algorithme plus simple et plus efficace pour cette famille de graphes. De plus, nous considérons les graphes planaires extérieurs. Nous donnons une formule pour trouver l'indice chromatique fort exact pour les graphes bipartis planaires extérieurs. Nous améliorons également la borne supérieure pour les graphes planaires extérieurs généraux. 4) Enfin, nous étudions les bicliques dans les graphes sans faux jumeaux et nous présentons ensuite un algorithme $O(n+m)$ pour reconnaître les graphes convergents et divergents en améliorant l'algorithme $O(n^4)$.
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Bai, Yandong. "Arc colorings and cycles in digraphs." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112356/document.
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Cette thèse étudie la coloration d'arcs et de cycles dans les graphes orientés. Elle se concentre sur les sujets suivants : la coloration propre d'arcs avec des sommet-distingué dans les graphes orientés, les cycles courts dans les graphes orientés avec des sous-graphes interdits, les cycles sommet-disjoints dans dans les tournois bipartis, les cycle-facteurs dans les tournois bipartis régulier et les arcs universels dans les tournois. La thèse est basée sur cinq articles originaux publiés ou présentés dans des journaux. Les principaux résultats sont les suivants. Nous introduisons la coloration propre d'arcs avec des sommet-distingué dans les graphes orientés. Nous avons proposé une conjecture sur le nombre arc-chromatique sommet-distingué et nous avons aussi donné quelque résultats partiels. Nous avons étendu un résultat de Razborov en prouvant que la conjecture de Caccetta-Häggkvist est vraie pour certains graphes orientés avec des sous-graphes interdits. Nous avons montré que chaque tournoi biparti avec degré sortant minimum au moins qr-1 contient r cycles de sommets-disjoints de toutes longueurs possibles. Le cas spécial q=2 confirme le cas du tournoi biparti de la conjecture de Bermond-Thomassen. Nous avons montré que chaque tournoi biparti k-régulier avec k>2 que l'on notera B a deux cycles complémentaires de longueurs 6 et |V(B)-6|, à moins que B soit isomorphe à un graphe spécifique, étayant ainsi une conjecture sur des 2-cycles-facteurs dans les tournois bipartis. En outre, nous montrons que tous les tournois bipartis réguliers ont un k-cycle-facteur. Nous donnons une condition nécessaire et suffisante pour l'existence d'un arc universel dans un tournoi et nous caractérisons tous les tournois où chaque arc est universelIn this thesis, we study arc colorings and cycles in digraphs. The following topics are considered: vertex-distinguishing proper arc colorings in digraphs, short cycles in digraphs with forbidden subgraphs , disjoint cycles in bipartite tournaments, cycle factors in regualr bipartite tournaments and universal arcs in tournaments. The main results are contained in five original articles published or submitted to an international journal. We introduce vertex-distinguishing proper arc colorings of digraphs. A conjecture on the vertex-distinguishing arc-chromatic number is given and some partial results are obtained. We extend a result of Razborov by proving that the Caccetta-Häggkvist conjecture is true for digraphs with certain induced forbidden subgraphs or with certain forbidden subgraphs. We show that every bipartite tournament with minimum outdegree at least qr-1 has r vertex disjoint cycles of any given possible lengths. The special case q=2 of the result verifies the bipartite tournament case of the Bermond-Thomassen conjecture. As a partial support of a conjecture on 2-cycle-factors in bipartite tournaments, we prove that every k-regular bipartite tournament B with k>2 has two complementary cycles of lengths 6 and |V(B)|-6, unless B is isomorphic to a special digraph. Besides, we show that every k-connected regular bipartite tournament has a k-cycle-factor. We also give a sufficient and necessary condition for the existence of a universal arc in a tournament and characterize all the tournaments in which every arc is universal
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Oliveira, Bruna Marcele Martins de. "Hemodinâmica uterina avaliada por ultrassom Doppler colorido e taxa de fertilidade de vacas submetidas à IATF com sêmen analisado por sondas fluorescentes." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/10/10131/tde-19072012-110306/.
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Após a inseminação artificial, as fêmeas apresentam reação inflamatória transitória e fisiológica, que pode resultar em alterações na vascularização uterina. A ultrassonografia Doppler colorido é uma técnica não invasiva, que vem sendo utilizada para estudar a hemodinâmica do trato reprodutivo de bovinos. Os objetivos deste trabalho foram verificar a resposta inflamatória uterina por ultrassonografia Doppler colorido e a taxa de fertilidade em bovinos após inseminação artificial (IA) com sêmen avaliado por sondas fluorescentes. Para isso foram delineados dois experimentos. O experimento 1 foi realizado para estudar a hemodinâmica uterina por ultrassonografia Doppler colorido em bovinos após a IA. Foram utilizadas 18 vacas da raça Nelore, submetidas a um protocolo para a inseminação artificial em tempo fixo (IATF) e divididas em dois grupos: Grupo não inseminado (controle, GC, n=9) e grupo submetido à inseminação artificial (GIA, n=9). Avaliações por ultrassonografia foram realizadas em cinco momentos em modo espectral (30 horas antes da IA, 4, 24, 48 e 168 horas após a IA) para avaliar o índice de resistência (RI) da artéria uterina e em quatro momentos em modo color Doppler (4, 24, 48 e 168 horas após a IA) para avaliar a vascularização dos cornos uterinos. O diagnóstico de gestação foi feito após 30 dias da IA. No experimento 2 objetivou-se verificar se o percentual de espermatozóides com integridade das membranas plasmática e acrossomal e função mitocondrial (PIAIC) avaliadas por sondas fluorescentes influencia a fertilidade e estudar a hemodinâmica uterina após a deposição do sêmen com diferentes percentuais de espermatozóides PIAIC. Foram utilizadas 182 vacas paridas da raça Nelore, submetidas a um protocolo para IATF e divididas em três grupos de acordo com a qualidade do sêmen: Bom (B) 44,5%, Médio (M) 23% e Regular (R) 8,5% de espermatozóides PIAIC/palheta. Uma amostra de 30% das fêmeas (54, sendo 18 de cada grupo) foram submetidas a avaliações com ultrassonografia Doppler colorido 30 horas antes da IA, 4 e 24 horas após a IA. Foram considerados os RI das artérias uterinas direita (AD) e esquerda (AE) e vascularização subjetiva dos cornos uterinos direito (CD) e esquerdo (CE). Posteriormente, foram separados levando em consideração o lado do ovário contendo o folículo dominante para comparar RI das artérias ipsi (AI) e contralateral (AC) e vascularização subjetiva dos cornos uterinos ipsi (CI) e contralateral (CC). O diagnóstico de gestação foi realizado 30 dias após a IA. Para a análise estatística foi utilizado o programa SAS versão 9.2 (SAS 2010). As variáveis foram analisadas pelo PROC MIXED, utilizando modelo linear misto para medidas repetidas no tempo. Foram considerados os efeitos fixos de grupo, tempo e interação grupo x tempo. Os dados obtidos foram submetidos à análise de variância e ao teste de Duncan, pelo PROC GLM. A análise de Qui-Quadrado foi utilizada para determinar a taxa de prenhez, de acordo com a qualidade do sêmen pelo PROC FREQ. O nível de significância considerado foi de 5%. No experimento 1 não foram observadas diferenças dos parâmetros avaliados por ultrassom Doppler entre GIA e GC, mas foram notados efeitos do tempo para RI, sendo mais baixos 4 horas após a IA. Quando os dados foram avaliados de acordo com o lado do folículo dominante foi observado que 4 e 24 horas após a IA, RI da AC do GIA foi mais baixo do que o GC. No experimento 2 não houve diferença entre os animais inseminados com sêmen B, M ou R quanto a hemodinâmica uterina, mas houve efeito do tempo, sendo que 4 horas após a IA verificou-se menor valor de RI e maior fluxo sanguíneo. A taxa de prenhez dos animais inseminados com o sêmen B (64,7%) foi maior quando comparada ao sêmen R (36,2%), sendo que ambos não diferiram do sêmen M (50,0%). Pode-se concluir que não é possível detectar por ultrassonografia Doppler alterações na hemodinâmica uterina devido à IA em fêmeas bovinas. A deposição de sêmen com diferentes qualidades não altera a hemodinâmica uterina de forma detectável por ultrassonografia Doppler em bovinos. Por outro lado, é possível detectar por ultrassonografia Doppler mudanças na perfusão sanguínea do útero em relação ao tempo da IA, o que pode ser devido a alterações hormonais que ocorrem durante o ciclo estral. Por fim, a IA com sêmen contendo menor percentual de espermatozoides PIAIC causa redução na taxa de fertilidade em bovinos.After insemination, females have physiological and transient inflammatory reaction, which can result in changes in the uterine vasculature. The color Doppler ultrasound is a noninvasive technique that has been used to study the hemodynamics of cattle reproductive tract.The purposes of this work were to verify uterine inflammatory response by color Doppler ultrasound and fertility rate in cattle after artificial insemination (IA) with semen evaluated by fluorescent probes. For this, two experiments were delineated. The first experiment was conducted to study the uterine hemodynamic by color Doppler ultrasound in cattle after AI. Were used 18 Nellore cows that were subjected to a protocol for fixed timed artificial insemination (IATF). The animals were divided in two groups: Not inseminated group (control, GC, n=9) and inseminated group (GIA, n=9). Ultrasonografic evaluation were done in five moments on spectral mode (30 hours before AI, 4, 24, 48 e 168 hours after IA) to evaluate the resistence index (RI) of uterine artery and in four moments in color Doppler mode to evaluate the uterine horns vascularization. The pregnancy diagnostic was done 30 days after IA. In the second experiment the objective was to evaluate whether the percentage of sperm with plasma membrane integrity and acrossomal and mitochondrial function (PIAIC) assessed by fluorescent probes influences fertility and study the uterine hemodynamic after the deposition of semen with different percentages of PIAIC sperm. Were used 182 caved Nellore cows submitted to a protocol for IATF and divided into three groups according to semen quality: Good (B) 44.5%, Medium (M) 23% and Regular (R) 8,5% of PIAIC sperm/blade. A sample of 30% of female (54, 18 in each group) were submitted to evaluation by color Doppler ultrasound 30 hours before IA, 4 and 24 hours after IA. Were considered RI of right (AD) and left (AE) uterine arteries and subjective vascularization of right (CD) and left (CE) uterine horns. Later, they were separated taking into account the side of the ovary containing the dominant follicle to compare RI of ipsi (AI) and contralateral (AC) arteries and subjective vascularization of ipsi (CI) and contralateral (CC) uterine horns. The pregnancy diagnostic was done 30 days after IA. Statistical analysis was performed using the program SAS version 9.2 (SAS 2010). The variables were analyzed by PROC MIXED, using mixed linear model for repeated measures in time. We considered effects of group, time and group x time interaction. The data obtained were submitted to ANOVA and Duncan test, using PROC GLM. The chi-square analysis was used to determine pregnancy rate, according to the quality of semen by PROC FREQ. the significance level was 5%. In experiment 1 there were no differences of the parameters evaluated by Doppler ultrasound between GIA and GC, but time effects were noted for RI, it was lower four hours after IA. When the data were evaluated according to the side of the dominant follicle was observed that 4 and 24 hours after IA, RI of AC of GIA was lower when it was compared with GC. In experiment 2 there was no difference between animals inseminated with semen B, M or R about uterine hemodynamics, but there were effects of time, so that 4 hours after IA showed lower value of RI and increased blood flow. The pregnancy rate of animals inseminated with semen B (64.7%) was higher when compared with semen R (36.2%), both of them did not differ of semen M (50.0%). It can be concluded that is not possible to detect uterine hemodynamic changes by Doppler ultrasound due to IA in cattle. The deposition of semen with different qualities does not change the uterine hemodynamics enough to be detectable by Doppler ultrasonography in cattle. On the other hand, is possible to detect changes in blood perfusion of the uterus in relation to the time of IA by Doppler ultrasound, which may be due to hormonal changes that occur during the estrous cycle. Finally, IA with semen containing a lower percentage of PIAIC sperm causes a reduction in fertility rate in cattle.
Books on the topic "Proper coloring"
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author, Kallman Ted, ed. Project management professionals are coloring outside the lines. Pittsburgh, Pennsylvania: COTL Press, 2015.
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Why Do You Talk So Proper: The Coloring Book. Indy Pub, 2022.
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son, oscar. 50 Animals Coloring Book: 50 Proper Designs Including Lions, Bears, Tigers, Snakes, Birds, Fish, and More Amazing Animals. Independently Published, 2020.
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Press, Johnson. Unicorns Coloring Book: Age Proper Foundations for Pre-School and Early Age Kids under 8 Years - Rainbows, Stars, Palaces, Knolls and Mushroom Houses. Independently Published, 2022.
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Chris, Miller. Amazing World of Dogs : Coloring Book for Adults: Amazing Coloring Book, Great Gift for Christmas, Perfect for Your Girlfriend, Relaxation Book to Calm You down, Proper for Adults and Teenagers, 30 Patterns,. Independently Published, 2019.
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Chris, Miller. Amazing World of Cats : Coloring Book for Adults: Amazing Coloring Book, Great Gift for Christmas, Perfect for Your Girlfriend, Relaxation Book to Calm You down, Proper for Adults and Teenagers, over 30 Patterns. Independently Published, 2019.
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Publication, Joyceby Hacbsk. My First Human Anatomy Coloring Book for Kids: A Complete Entertaining and Instructive Book to Human Physiology and How Anatomy Work with 60 Page for Learning Proper Name of Anatomy and Page for Drawing -Gift for Medical School and College Student. Independently Published, 2020.
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Publication, Joyceby Hacbsk. Human Anatomy Coloring Book for Kids: This Entertaining and Instructive Guide to the Human Physiology and How Anatomy Work with 60 Page for Learning or Writing Proper Name of Anatomy and Page for Drawing - Gift for School and Medical College Student. Independently Published, 2020.
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Bandit, Coloring. Construire Votre Propre Bande Dessinée: Livre de Coloriage pour Filles 6 Ans. Coloring Bandit, 2017.
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Copeland, Rita. Emotion and the History of Rhetoric in the Middle Ages. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192845122.001.0001.
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Rhetoric is an engine of social discourse and the art charged with generating and swaying emotion. The history of rhetoric provides a continuous structure by which we can measure how emotions were understood, articulated, and mobilized under various historical circumstances and social contracts. This book is about how rhetoric in the West from Late Antiquity to the later Middle Ages represented the role of emotion in shaping persuasions. It is the first book-length study of medieval rhetoric and the emotions, coloring in what has largely been a blank space between about 600 CE and the cusp of early modernity. Rhetoric in the Middle Ages, as in other periods, constituted the gateway training for anyone engaged in emotionally persuasive writing. Medieval rhetorical thought on emotion has multiple strands of influence and sedimentations of practice. The earliest and most persistent tradition treated emotional persuasion as a property of surface stylistic effect, which can be seen in the medieval rhetorics of poetry and prose, and in literary production. But the impact of Aristotelian rhetoric, which reached the Latin West in the thirteenth century, gave emotional persuasion a core role in reasoning, incorporating it into the key device of proof, the enthymeme. In Aristotle, medieval teachers and writers found a new rhetorical language to explain the social and psychological factors that affect an audience. With Aristotelian rhetoric, the emotions became political. The impact of Aristotle’s rhetorical approach to emotions was to be felt in medieval political treatises, in poetry, and in preaching.
Book chapters on the topic "Proper coloring"
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Agnarsson, Geir, Ágúst S. Egilsson, and Magnús M. Halldórsson. "Proper Down-Coloring Simple Acyclic Digraphs." In Applications of Graph Transformations with Industrial Relevance, 299–312. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-25959-6_22.
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Chandran, L. Sunil, Sajal K. Das, Pavol Hell, Sajith Padinhatteeri, and Raji R. Pillai. "Template-Driven Rainbow Coloring of Proper Interval Graphs." In Algorithms and Discrete Applied Mathematics, 452–70. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67899-9_36.
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Bliznets, Ivan, and Danil Sagunov. "Two Generalizations of Proper Coloring: Hardness and Approximability." In Lecture Notes in Computer Science, 82–93. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-22105-7_8.
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Hocquard, Hervé, Dimitri Lajou, and Borut Lužar. "Between Proper and Strong Edge-Colorings of Subcubic Graphs." In Lecture Notes in Computer Science, 355–67. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48966-3_27.
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Pilipczuk, Michał, and Sebastian Siebertz. "Polynomial bounds for centered colorings on proper minor-closed graph classes." In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, 1501–20. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2019. http://dx.doi.org/10.1137/1.9781611975482.91.
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Barish, Robert D., and Tetsuo Shibuya. "The Fine-Grained Complexity of Approximately Counting Proper Connected Colorings (Extended Abstract)." In Combinatorial Optimization and Applications, 123–36. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-49614-1_8.
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"Proper Coloring." In Encyclopedia of Operations Research and Management Science, 1187. Boston, MA: Springer US, 2013. http://dx.doi.org/10.1007/978-1-4419-1153-7_200656.
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Sandefur, James T. "Introduction to dynamic modelling." In Discrete Dynamical Modeling, 1–54. Oxford University PressNew York, NY, 1993. http://dx.doi.org/10.1093/oso/9780195084382.003.0001.
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Abstract Dynamics is the study of how quantities change over time. Dynamic modeling is the process of developing a mathematical relationship that in some sense describes how a real world quantity changes over time. We do not claim that the mathematics gives an exact description of reality. But we do hope the analysis will give us some insight into the phenomenon being studied. Let’s begin by developing a simple model of how medicine is eliminated from the body. An empty container will represent the body. Add 4 cups of water to the container to model the blood in the body. Suppose we are going to take some medicine internally. Let’s assume that the proper dose of this medicine, say cough syrup, is 16 ml. To model this, add 16 ml of food coloring to the container. See figure 1.1. (To be precise, the 16 ml of food coloring should be added first, with enough water added to make a total of 4 cups of liquid.) How do the kidneys remove impurities from the blood? Loosely speaking, during any 4-hour period, the kidneys take in a fixed percentage of the blood and remove the medicine from that blood. Let’s assume the kidneys purify one-fourth of the blood during any 4-hour period.
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CRISTINA COSTA, ROSA, and JEAN CARLOS MIRANDA. "PRODUÇÃO DE JOGO DIDÁTICO SOBRE CORPO HUMANO PARA O ENSINO DE CIÊNCIAS/BIOLOGIA." In Itinerários de resistência: pluralidade e laicidade no Ensino de Ciências e Biologia. Editora Realize, 2021. http://dx.doi.org/10.46943/viii.enebio.2021.01.462.
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O TERMO LÚDICO TEM ORIGEM LATINA (LUDUS) E SIGNIFICA JOGO E BRINCADEIRA. PODEMOS ATRIBUIR TAMBÉM OS TERMOS ENTRETENIMENTO E DIVERSÃO, QUE SÃO ATIVIDADES LIGADAS AO PRAZER, POIS, ALÉM DE PROPORCIONAREM UMA SENSAÇÃO DE BEM-ESTAR, OS JOGOS FACILITAM A SOCIALIZAÇÃO E O CUMPRIMENTO DE REGRAS, MELHORANDO O CONVÍVIO SOCIAL. O LÚDICO, ANTES RESTRITO À EDUCAÇÃO INFANTIL E AO PRIMEIRO SEGMENTO DO ENSINO FUNDAMENTAL, TEM SIDO UTILIZADO TAMBÉM NO SEGUNDO SEGMENTO DO ENSINO FUNDAMENTAL, E NO ENSINO MÉDIO, DEVIDO À POSSIBILIDADE DE CONSTRUÇÃO DO CONHECIMENTO POR MEIO DE ATIVIDADES DINÂMICAS ONDE OS DISCENTES INTERAGEM ENTRE SI E COM O PROFESSOR, FACILITANDO A APRENDIZAGEM E SUA COMPREENSÃO DO MUNDO. UMA DAS FORMAS DE O PROFESSOR MANTER O INTERESSE DOS DISCENTES NAS AULAS, É UTILIZAR FERRAMENTAS QUE OS MOTIVEM E, AO MESMO TEMPO, FAVOREÇAM A CONSTRUÇÃO DO CONHECIMENTO. NESSE CONTEXTO, OS JOGOS DIDÁTICOS CONFIGURAM-SE COMO ATIVIDADES QUE DESAFIAM, CRIAM POSSIBILIDADES E FOMENTAM O APRENDIZADO. O PRESENTE TRABALHO APRESENTA O JOGO DIDÁTICO “CORPO HUMANO E IMAGEM”, PRODUZIDO COM VISTAS À UTILIZAÇÃO COMO FERRAMENTA AUXILIAR NA ABORDAGEM DO TEMA CORPO HUMANO, NA DISCIPLINA CIÊNCIAS/BIOLOGIA. A PESQUISA FOI REALIZADA NO COLÉGIO ESTADUAL RUI GUIMARÃES DE ALMEIDA (CERGA), UMA ESCOLA DA REDE ESTADUAL DE ENSINO, LOCALIZADA EM SANTO ANTÔNIO DE PÁDUA, REGIÃO NOROESTE DO ESTADO DO RIO DE JANEIRO. O CERGA ATENDE A ALUNOS DO ENSINO MÉDIO DO CURSO DE FORMAÇÃO DE PROFESSORES E DO ENSINO MÉDIO REGULAR (FORMAÇÃO GERAL). O CURSO DE FORMAÇÃO DE PROFESSORES FUNCIONA EM HORÁRIO INTEGRAL E POSSUÍA, EM 2018, TRÊS TURMAS, UMA DE CADA ANO DO ENSINO MÉDIO. INICIALMENTE, FOI ELABORADO UM QUESTIONÁRIO COM O OBJETIVO DE IDENTIFICAR AS DIFICULDADES DOS DISCENTES DO ENSINO MÉDIO DO CURSO DE FORMAÇÃO DE PROFESSORES EM RELAÇÃO AO CONTEÚDO DE BIOLOGIA, NO INTUITO DE INSTRUMENTALIZÁ-LOS PARA ATUAÇÃO NA DOCÊNCIA EM CIÊNCIAS, COM ÊNFASE NOS TEMAS CONSIDERADOS POR ELES COMO OS DE MAIOR COMPLEXIDADE, E PROPOR UMA FERRAMENTA PARA UTILIZAÇÃO, POR ELES, COM DISCENTES DO 5º ANO DO ENSINO FUNDAMENTAL I. A ANÁLISE DAS RESPOSTAS DOS DISCENTES INDICOU O TEMA CORPO HUMANO COMO O QUE ELES APRESENTAM MAIOR DIFICULDADE DE ASSIMILAÇÃO. POR ESSA RAZÃO, FOI DESENVOLVIDO O JOGO DIDÁTICO INTITULADO “CORPO HUMANO E IMAGEM”, INSPIRADO NO JOGO IMAGEM E AÇÃO® (GROW®).O KIT DO JOGO DIDÁTICO “CORPO HUMANO E IMAGEM” É COMPOSTO POR 1 TABULEIRO COM 80 CASAS, 4 PEÕES COLORIDOS (LARANJA, AZUL, ROSA E VERDE), 40 CARTAS-PERGUNTA, UMA FICHA CONTENDO AS RESPOSTAS DAS QUESTÕES DAS CARTAS-PERGUNTA, UM MANUAL DE REGRAS, UM DADO DE 6 FACES, UMA AMPULHETA (COM O TEMPO DE APROXIMADAMENTE 1 MINUTO) PARA MARCAR O TEMPO PARA RESPOSTA, 4 QUADROS BRANCOS PEQUENOS E 4 PINCÉIS PARA QUADRO BRANCO, NAS CORES DOS PEÕES. AS PERGUNTAS DO JOGO FORAM PRODUZIDAS A PARTIR DE LIVROS DO ENSINO FUNDAMENTAL I (5º ANO) ADOTADOS PELA REDE MUNICIPAL DE ENSINO DE SANTO ANTÔNIO DE PÁDUA (RJ). PARA A CONFECÇÃO DAS CARTAS-PERGUNTA, FORAM UTILIZADOS, ALÉM DOS LIVROS DIDÁTICOS, NOTEBOOK, IMPRESSORA COLORIDA, PAPEL CARTÃO E UMA PLASTIFICADORA. CADA CARTA-PERGUNTA CONTÊM UMA INFORMAÇÃO SOBRE UM ÓRGÃO, SISTEMA OU OUTRA ESTRUTURA DO CORPO HUMANO E O ALUNO QUE É O DESENHISTA DA VEZ, DEVE IDENTIFICAR E DESENHAR A RESPOSTA CORRETA PARA QUE O SEU GRUPO, AO OLHAR O DESENHO, ACERTE A RESPOSTA. O JOGO “CORPO HUMANO E IMAGEM” SEGUE A SEGUINTE DINÂMICA: A TURMA É DIVIDIDA EM ATÉ 4 EQUIPES; CADA EQUIPE ESCOLHE UM PEÃO COLORIDO (LARANJA, AZUL, ROSA E VERDE); CADA EQUIPE RECEBE 1 QUADRO BRANCO E 1 PINCEL PARA QUADRO BRANCO NA COR ESCOLHIDA; APÓS A DIVISÃO DA TURMA EM EQUIPES, É FEITO O LANÇAMENTO DO DADO PARA DEFINIÇÃO DA ORDEM DE PARTICIPAÇÃO DAS EQUIPES; O MEDIADOR (PROFESSOR) EMBARALHA AS CARTAS E COLOCA COM A FACE DAS PERGUNTAS VOLTADAS PARA BAIXO; ELE APANHA A PRIMEIRA CARTA DA PILHA E ENTREGA PARA UM MEMBRO DA PRIMEIRA EQUIPE, QUE TERÁ O TEMPO DE UMA AMPULHETA PARA FAZER O DESENHO REFERENTE A PERGUNTA E SEU GRUPO ACERTAR A RESPOSTA; A CADA RODADA UM COMPONENTE DO GRUPO É O DESENHISTA QUE TENTA PASSAR À SUA EQUIPE A RESPOSTA DA QUESTÃO, EM FORMA DE DESENHO. É PROIBIDO FALAR, ESCREVER LETRAS E/OU NÚMEROS E FAZER GESTOS E/OU MÍMICAS. EM CASO DE ACERTO, A EQUIPE LANÇA O DADO E ANDA O NÚMERO DE CASAS CORRESPONDENTE, A VEZ PASSA PARA A EQUIPE SEGUINTE E A CARTA-PERGUNTA VAI PARA A PILHA DE DESCARTE. EM CASO DE ERRO, A EQUIPE NÃO LANÇA O DADO, A VEZ PASSA PARA A EQUIPE SEGUINTE E A CARTA-PERGUNTA VAI PARA O FINAL DA PILHA. SE, AO ANDAR PELO TABULEIRO, O PEÃO CAIR NAS CASAS DE COR AZUL CLARO, A EQUIPE TEM DIREITO A MAIS UM LANÇAMENTO DO DADO E ANDA O NÚMERO DE CASAS CORRESPONDENTES; SE O PEÃO CAIR NAS CASAS DE COR PRETA, A EQUIPE FICA UMA RODADA SEM JOGAR. O JOGO SEGUE ESSA DINÂMICA ATÉ QUE UMA DAS EQUIPES ATINJA A CASA “CHEGADA”.
Conference papers on the topic "Proper coloring"
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Andrade, Davi de, and Ana Silva. "(Sub)Fall Coloring and B-Coloring Parameterized by Treewidth." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2022. http://dx.doi.org/10.5753/etc.2022.222982.
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Given a proper coloring f of G, a vertex u is a b-vertex if it is adjacent to every color class distinct from its own. It is said to be a b-coloring if each color class contains at least one b-vertex, and a fall coloring if all vertices are b-vertices. Also, if f is a fall coloring of an induced subgraph H of G, then we say that f is a subfall coloring of G. In this paper, we provide algorithms for each of the decision problems related to these colorings whose running times are FPT when parameterized by the number of colors plus the treewidth of the input graph.
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Bai, Xuqing, Xueliang Li, and Yindi Weng. "The Colored Disconnection Numbers of Cellular and Grid Networks." In 2nd International Conference on Soft Computing, Artificial Intelligence and Machine Learning (SAIM 2021). AIRCC Publishing Corporation, 2021. http://dx.doi.org/10.5121/csit.2021.111009.
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Let G be a nontrivial link-colored connected network. A link-cut R of G is called a rainbow link-cut if no two of its links are colored the same. A link-colored network G is rainbow disconnected if for every two nodes u and v of G, there exists a u-v rainbow link-cut separating them. Such a link coloring is called a rainbow disconnection coloring of G. For a connected network G, the rainbow disconnection number of G, denoted by rd(G), is defined as the smallest number of colors that are needed in order to make G rainbow disconnected. Similarly, there are some other new concepts of network colorings, such as proper disconnection coloring, monochromatic disconnection coloring and rainbow node-disconnection coloring. In this paper, we obtain the exact values of the rainbow (node-)disconnection numbers, proper and monochromatic disconnection numbers of cellular networks and grid networks, respectively.
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An, Zhuomo, Shuangliang Tian, and Cai Jin. "Proper additive coloring of Special Graphs." In 2020 International Conference on Computer Science and Management Technology (ICCSMT). IEEE, 2020. http://dx.doi.org/10.1109/iccsmt51754.2020.00015.
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Jose, Sabitha, and Sudev Naduvath. "On equitable near proper coloring of certain graph classes." In 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108430.
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Arputhamary, I. Annammal, R. Revathi, and D. Angel. "On Strong Proper Connected Coloring of Generalised Friendship Graphs." In 2022 Third International Conference on Intelligent Computing Instrumentation and Control Technologies (ICICICT). IEEE, 2022. http://dx.doi.org/10.1109/icicict54557.2022.9917925.
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Araújo, Júlio, and Alexandre Cezar. "On (acyclic) proper orientations and the cartesian product." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2023. http://dx.doi.org/10.5753/etc.2023.230546.
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Given an orientation D of the edges of a simple graph G, the indegree of a vertex v ∈ V(G), dD(v), is the number of arcs with head in v. Such orientation induces a coloring φ(v) = dD(v) + 1 of G. We say that D is a proper k-orientation if φ is a proper (k + 1)-coloring of G. The proper orientation number of G, denoted by X(G), is the least positive integer k such that G admits a proper k-orientation. We study a variation of this problem where we consider the orientation D to be acyclic. To the best of our knowledge this is the first article considering this variation. Furthermore, we also study the parameter X for graphs obtained by the cartesian product of graphs, introducing the concept of discordant set of proper orientations, that is a set where in different orientations, the same vertex has different indegrees.
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Dudas, Adam, and Bianka Modrovicova. "Decision Trees in Proper Edge k-coloring of Cubic Graphs." In 2023 33rd Conference of Open Innovations Association (FRUCT). IEEE, 2023. http://dx.doi.org/10.23919/fruct58615.2023.10143001.
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Andrade, Davi de, and Ana Silva. "On the Complexity of Subfall Coloring of Graphs." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2021. http://dx.doi.org/10.5753/etc.2021.16383.
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Given a graph G and a proper k-coloring f of G, a b-vertex in f is a vertex that is adjacent to every color class but its own. If every vertex is a b-vertex, then f is a fall k-coloring; and G has a subfall k-coloring if there is an induced H $\subseteq$ G such that H has a fall k-coloring. The subfall chromatic number of G is the largest positive integer $\psi_{fs}(G)$ such that G has a subfall $\psi_{fs}(G)$-coloring. We prove that deciding if a graph G has a subfall k-coloring is NP-complete for k $\geq$ 4, and characterize graphs having a subfall 3-coloring. This answers a question posed by Dunbar et al. (2000) in their seminal paper. We also prove polinomiality for chordal graphs and cographs, and present a comparison with other known coloring metrics based on heuristics.
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Rocha, Aleffer, Sheila M. Almeida, and Leandro M. Zatesko. "The Rainbow Connection Number of Triangular Snake Graphs." In Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/etc.2020.11091.
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Rainbow coloring problems, of noteworthy applications in Information Security, have been receiving much attention last years in Combinatorics. The rainbow connection number of a graph G is the least number of colors for a (not necessarily proper) edge coloring of G such that between any pair of vertices there is a path whose edge colors are all distinct. In this paper we determine the rainbow connection number of the triple triangular snake graphs.
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Svistunova, Victoria Romanovna. "Comparison of encodings and optimization of parameters of SAT-solver in graph coloring problem." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-61.
Full textAbstract:
The paper considers the problem of coloring graphs of a special type, reduction of this problem to the problem of satisfiability of Boolean formulas (SAT) and optimization of the parameters of the SAT solver, which allows solving problems of such view in less time. The problem of the existence of a proper coloring graph G in k colors is, generally speaking, NP-complete for k >= 3, and can be reduced in various ways to another well-known NP-complete problem - the problem of satisfiability of Boolean formulas in conjunctive normal form. The efficiency of the work can depend on the encoding SAT solvers (specialized programs for solving a problem feasibility). The parameters of the SAT solver Glucose were optimized using the genetic algorithm implemented in the PyDGGA package. Optimization made it possible to speed up Glucose by 3-5 times.
Reports on the topic "Proper coloring"
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Palamar, Svitlana P., Ganna V. Bielienka, Tatyana O. Ponomarenko, Liudmyla V. Kozak, Liudmyla L. Nezhyva, and Andrei V. Voznyak. Formation of readiness of future teachers to use augmented reality in the educational process of preschool and primary education. CEUR Workshop Proceedings, July 2021. http://dx.doi.org/10.31812/123456789/4636.
Full textAbstract:
The article substantiates the importance of training future teachers to use AR technologies in the educational process of preschool and primary education. Scientific sources on the problem of AR application in education are analyzed. Possibilities of using AR in work with preschoolers and junior schoolchildren are considered. Aspects of research of the problem of introduction of AR in education carried out by modern foreign and domestic scientists are defined, namely: use of AR-applications in education; introduction of 3D technologies, virtual and augmented reality in the educational process of preschool and primary school; 3D, virtual and augmented reality technologies in higher education; increase of the efficiency of learning and motivating students through the use of AR-applications on smartphones; formation of reading culture by means of augmented reality technology; prospects for the use of augmented reality within the linguistic and literary field of preschool and primary education. The authors analyzed the specifics of toys with AR-applications, interactive alphabets, coloring books, encyclopedias and art books of Ukrainian and foreign writers, which should be used in working with children of preschool and primary school age; the possibilities of books for preschool children created with the help of augmented reality technologies are demonstrated. The relevance of the use of AR for the effective education and development of preschoolers and primary school children is determined. Problems in the application of AR in the educational process of modern domestic preschool education institutions are outlined. A method of diagnostic research of the level and features of readiness of future teachers to use AR in the educational process of preschool and primary education has been developed. Criteria, indicators are defined, the levels of development of the main components of the studied readiness (motivational, cognitive, activity) are characterized. The insufficiency of its formation in future teachers in the field of preschool and primary education; inconsistency between the peculiarities of training future teachers to use AR in professional activities and modern requirements for the quality of the educational process; the need to develop and implement a holistic system of formation of the studied readiness of future teachers in the conditions of higher pedagogical education are proved. A model of forming the readiness of future teachers to use AR in the educational process of preschool and primary education has been developed.