Letteratura scientifica selezionata sul tema "Packing chromatic number"
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Articoli di riviste sul tema "Packing chromatic number":
Brešar, Boštjan, Sandi Klavžar, Douglas F. Rall e Kirsti Wash. "Packing chromatic number versus chromatic and clique number". Aequationes mathematicae 92, n. 3 (13 dicembre 2017): 497–513. http://dx.doi.org/10.1007/s00010-017-0520-9.
Durgun, Derya, e Busra Ozen-Dortok. "Packing chromatic number of transformation graphs". Thermal Science 23, Suppl. 6 (2019): 1991–95. http://dx.doi.org/10.2298/tsci190720363d.
Balogh, József, Alexandr Kostochka e Xujun Liu. "Packing chromatic number of cubic graphs". Discrete Mathematics 341, n. 2 (febbraio 2018): 474–83. http://dx.doi.org/10.1016/j.disc.2017.09.014.
Ekstein, Jan, Přemysl Holub e Bernard Lidický. "Packing chromatic number of distance graphs". Discrete Applied Mathematics 160, n. 4-5 (marzo 2012): 518–24. http://dx.doi.org/10.1016/j.dam.2011.11.022.
Torres, Pablo, e Mario Valencia-Pabon. "The packing chromatic number of hypercubes". Discrete Applied Mathematics 190-191 (agosto 2015): 127–40. http://dx.doi.org/10.1016/j.dam.2015.04.006.
William, Albert, Roy Santiago e Indra Rajasingh. "Packing Chromatic Number of Cycle Related Graphs". International Journal of Mathematics and Soft Computing 4, n. 1 (1 gennaio 2014): 27. http://dx.doi.org/10.26708/ijmsc.2014.1.4.04.
Torres, Pablo, e Mario Valencia-Pabon. "On the packing chromatic number of hypercubes". Electronic Notes in Discrete Mathematics 44 (novembre 2013): 263–68. http://dx.doi.org/10.1016/j.endm.2013.10.041.
Ferme, Jasmina. "A characterization of 4-χρ-(vertex-)critical graphs". Filomat 36, n. 19 (2022): 6481–501. http://dx.doi.org/10.2298/fil2219481f.
Lemdani, Rachid, Moncef Abbas e Jasmina Ferme. "Packing chromatic numbers of finite super subdivisions of graphs". Filomat 34, n. 10 (2020): 3275–86. http://dx.doi.org/10.2298/fil2010275l.
CHALUVARAJU, B., e M. KUMARA. "The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs". Journal of Ultra Scientist of Physical Sciences Section A 33, n. 5 (23 agosto 2021): 66–73. http://dx.doi.org/10.22147/jusps-a/330501.
Tesi sul tema "Packing chromatic number":
Mortada, Maidoun. "The b-chromatic number of regular graphs". Thesis, Lyon 1, 2013. http://www.theses.fr/2013LYO10116.
Two problems are considered in this thesis: the b-coloring problem and the graph packing problem. 1. The b-Coloring Problem : A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least a vertex in each other color class. The b-chromatic number of a graph G, denoted by b(G), is the maximum number t such that G admits a b-coloring with t colors. El Sahili and Kouider asked whether it is true that every d-regular graph G with girth at least 5 satisfies b(G) = d + 1. Blidia, Maffray and Zemir proved that the conjecture is true for d ≤ 6. Also, the question was solved for d-regular graphs with supplementary conditions. We study El Sahili and Kouider conjecture by determining when it is possible and under what supplementary conditions it is true. We prove that b(G) = d+1 if G is a d-regular graph containing neither a cycle of order 4 nor of order 6. Then, we provide specific conditions on the vertices of a d-regular graph G with no cycle of order 4 so that b(G) = d + 1. Cabello and Jakovac proved that if v(G) ≥ 2d3 - d2 + d, then b(G) = d + 1, where G is a d-regular graph. We improve this bound by proving that if v(G) ≥ 2d3 - 2d2 + 2d, then b(G) = d+1 for a d-regular graph G. 2. Graph Packing Problem : Graph packing problem is a classical problem in graph theory and has been extensively studied since the early 70's. Consider a permutation σ : V (G) → V (Kn), the function σ* : E(G) → E(Kn) such that σ *(xy) = σ *(x) σ *(y) is the function induced by σ. We say that there is a packing of k copies of G into the complete graph Kn if there exist k permutations σ i : V (G) → V (Kn), where i = 1,…, k, such that σ*i (E(G)) ∩ σ*j (E(G)) = ɸ for I ≠ j. A packing of k copies of a graph G will be called a k-placement of G. The kth power Gk of a graph G is the supergraph of G formed by adding an edge between all pairs of vertices of G with distance at most k. Kheddouci et al. proved that for any non-star tree T there exists a 2-placement σ on V (T). We introduce a new variant of graph packing problem, called the labeled packing of a graph into its power graph
Tarhini, Batoul. "Oriented paths in digraphs and the S-packing coloring of subcubic graph". Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCK079.
This PhD thesis is divided into two principal parts: Part I delves into the existenceof oriented paths in digraphs, aiming to establish a connection between a digraph'schromatic number and the existence of specific oriented paths within it as subdigraphs. Digraphs contained in any n-chromatic digraph are called n-universal. We consider two conjectures: Burr's conjecture, which states that every oriented tree of order n is (2n-2)-universal, and El Sahili's conjeture which states that every oriented path of order n is n-universal. For oriented paths in general, the best bound is given by Burr, that is every oriented path of order n is (n − 1)^2-universal. Our objective is to study the existence of an integer k such that any digraph with a chromatic number k, contains a copy of a given oriented path with three blocks as its subdigraph. To achieve our goals, we rely significantly on fundamental concepts, including, induction on the order of a given digraph, final forests, leveling techniques, and strategic digraph decomposition methods. A path P (k1, k2, k3) is an oriented path consisting of k1 forward arcs, followed by k2 backward arcs, and then by k3 forward arcs. For the path P(k,1,l), we have confirmed El Sahili's conjecture in Hamiltonian digraphs. More clearly, we have established the existence of any path P (k, 1, l) of order n in any n-chromatic Hamiltonian digraph. And depending on this result concerning Hamiltonian digraphs, we proved the correctness of El Sahili's conjecture on a more general class of digraphs which is digraphs containing a Hamiltonian directed path. We introduce a new technique which is represented by a decomposition of the digraph into subdigraphs defined by a series of successive operations applied to the digraph relying on the famous theorem of Roy which establishes the existence of a directed path of order n in any n-chromatic digraph. This technique has proven to be instrumental in establishing new linear bounds for the chromatic number of digraphs that lack an oriented path with three blocks. In deed, using this technique, we proved that the path P(k,1,l) satisfies Burr's conjecture.Moreover, for any path with three blocks, P(k,l,r) we establish a linear bound for the chromatic number which improves all the previously reached bounds. In Part II we study the problem of S-packing coloring in graphs. Given a non-decreasing sequence S = (s1, s2, . . . , sk) of positive integers, an S-packing coloring of a graph G is a partition of the vertex set of G into k subsets{V1, V2, . . . , Vk} such that for each 1 ≤ i ≤ k, the distance between any two dis-tinct vertices u and v in Vi is at least si + 1. Our focus is centered on an intriguing conjecture proposed by Brešar et al., which states that packing chromatic number of the subdivision of any subcubic graph is at most 5. Our desired aim is to provide a confirmation of this conjecture for specific classes of subcubic graphs, and to address the unresolved issues raised within this subject matter. An observation for Gastineau and Togni states that if a graph G is (1, 1, 2, 2)-packing colorable, then the chromatic number of its subdivision graph S(G) is at most 5, and hence it satisfies the conjecture. Depending on this observation, and in order to prove the correctness of the conjecture for the class of cubic Halin graphs, we studied its S-packing coloring aiming to prove that it admits a (1, 1, 2, 2)- packing coloring. We proved that a cubic Halin graph is (1, 1, 2, 3)-packing colorable, then it is (1, 1, 2, 2)-packing colorable, and so we confirm the conjecture for this class. Moreover, Gastineau and Togni, after proving that every subcubic graph is (1, 2, 2, 2, 2, 2, 2)-packing colorbale, have posed an open problem on whether every subcubic graph is (1, 2, 2, 2, 2, 2)-packing colorable. We answer this question in affirmative in the particular class we worked on; we proved that cubic Halin graphs are (1, 2, 2, 2, 2, 2)-packing colorable
Moustrou, Philippe. "Geometric distance graphs, lattices and polytopes". Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0802/document.
A distance graph G(X;D) is a graph whose set of vertices is the set of points X of a metric space (X; d), and whose edges connect the pairs fx; yg such that d(x; y) 2 D. In this thesis, we consider two problems that may be interpreted in terms of distance graphs in Rn. First, we study the famous sphere packing problem, in relation with thedistance graph G(Rn; (0; 2r)) for a given sphere radius r. Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor log log n for infinitely many dimensions n. We prove an effective version of this result, in the sense that we exhibit, for the same set of dimensions, finite families of lattices containing a lattice reaching this bound. Our construction uses codes over cyclotomic fields, lifted to lattices via Construction A. We also prove a similar result for families of symplectic lattices. Second, we consider the unit distance graph G associated with a norm k _ k. The number m1 (Rn; k _ k) is defined as the supremum of the densities achieved by independent sets in G. If the unit ball corresponding with k _ k tiles Rn by translation, then it is easy to see that m1 (Rn; k _ k) > 1 2n . C. Bachoc and S. Robins conjectured that the equality always holds. We show that this conjecture is true for n = 2 and for several Voronoï cells of lattices in higher dimensions, by solving packing problems in discrete graphs
Changiz, Rezaei Seyed Saeed. "Entropy and Graphs". Thesis, 2014. http://hdl.handle.net/10012/8173.
Capitoli di libri sul tema "Packing chromatic number":
Subercaseaux, Bernardo, e Marijn J. H. Heule. "The Packing Chromatic Number of the Infinite Square Grid is 15". In Tools and Algorithms for the Construction and Analysis of Systems, 389–406. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30823-9_20.
Wang, Hong, e Norbert Sauer. "The Chromatic Number of the Two-Packing of a Forest". In The Mathematics of Paul Erdős II, 143–66. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7254-4_12.
Wang, Hong, e Norbert Sauer. "The Chromatic Number of the Two-packing of a Forest". In Algorithms and Combinatorics, 99–120. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60406-5_11.
Bianchi, Marco E. "|The HMG-box domain". In DNA-Protein: Structural Interactions, 177–200. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780199634545.003.0007.
Atti di convegni sul tema "Packing chromatic number":
Kühn, Daniela, e Deryk Osthus. "Critical chromatic number and the complexity of perfect packings in graphs". In the seventeenth annual ACM-SIAM symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1109557.1109651.