Relevant bibliographies by topics / Random graphs

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Random graphs'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 October 2024

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Journal articles on the topic "Random graphs"

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FÜRER, MARTIN, and SHIVA PRASAD KASIVISWANATHAN. "Approximately Counting Embeddings into Random Graphs." Combinatorics, Probability and Computing 23, no. 6 (July 9, 2014): 1028–56. http://dx.doi.org/10.1017/s0963548314000339.

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LetHbe a graph, and letCH(G) be the number of (subgraph isomorphic) copies ofHcontained in a graphG. We investigate the fundamental problem of estimatingCH(G). Previous results cover only a few specific instances of this general problem, for example the case whenHhas degree at most one (the monomer-dimer problem). In this paper we present the first general subcase of the subgraph isomorphism counting problem, which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labelling of the vertices such that every edge is between vertices with different labels, and for every vertex all neighbours with a higher label have identical labels. The labelling implicitly generates a sequence of bipartite graphs, which permits us to break the problem of counting embeddings of large subgraphs into that of counting embeddings of small subgraphs. Using this method, we present a simple randomized algorithm for the counting problem. For all decomposable graphsHand all graphsG, the algorithm is an unbiased estimator. Furthermore, for all graphsHhaving a decomposition where each of the bipartite graphs generated is small and almost all graphsG, the algorithm is a fully polynomial randomized approximation scheme.We show that the graph classes ofHfor which we obtain a fully polynomial randomized approximation scheme for almost allGincludes graphs of degree at most two, bounded-degree forests, bounded-width grid graphs, subdivision of bounded-degree graphs, and major subclasses of outerplanar graphs, series-parallel graphs and planar graphs of large girth, whereas unbounded-width grid graphs are excluded. Moreover, our general technique can easily be applied to proving many more similar results.
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McDiarmid, C. "RANDOM GRAPHS." Bulletin of the London Mathematical Society 19, no. 3 (May 1987): 273. http://dx.doi.org/10.1112/blms/19.3.273a.

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Ruciński, A. "Random graphs." ZOR Zeitschrift für Operations Research Methods and Models of Operations Research 33, no. 2 (March 1989): 145. http://dx.doi.org/10.1007/bf01415170.

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Borbély, József, and András Sárközy. "Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)." Uniform distribution theory 14, no. 2 (December 1, 2019): 103–26. http://dx.doi.org/10.2478/udt-2019-0017.

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AbstractIn the last decades many results have been proved on pseudo-randomness of binary sequences. In this series our goal is to show that using many of these results one can also construct large families of quasi-random, pseudo-random and strongly pseudo-random graphs. Indeed, it will be proved that if the first row of the adjacency matrix of a circulant graph forms a binary sequence which possesses certain pseudorandom properties (and there are many large families of binary sequences known with these properties), then the graph is quasi-random, pseudo-random or strongly pseudo-random, respectively. In particular, here in Part I we will construct large families of quasi-random graphs along these lines. (In Parts II and III we will present and study constructions for pseudo-random and strongly pseudo-random graphs, respectively.)
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Gao, Yong. "Treewidth of Erdős–Rényi random graphs, random intersection graphs, and scale-free random graphs." Discrete Applied Mathematics 160, no. 4-5 (March 2012): 566–78. http://dx.doi.org/10.1016/j.dam.2011.10.013.

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KOHAYAKAWA, YOSHIHARU, GUILHERME OLIVEIRA MOTA, and MATHIAS SCHACHT. "Monochromatic trees in random graphs." Mathematical Proceedings of the Cambridge Philosophical Society 166, no. 1 (January 16, 2018): 191–208. http://dx.doi.org/10.1017/s0305004117000846.

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AbstractBal and DeBiasio [Partitioning random graphs into monochromatic components, Electron. J. Combin.24(2017), Paper 1.18] put forward a conjecture concerning the threshold for the following Ramsey-type property for graphsG: everyk-colouring of the edge set ofGyieldskpairwise vertex disjoint monochromatic trees that partition the whole vertex set ofG. We determine the threshold for this property for two colours.
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Whittle, P. "Random fields on random graphs." Advances in Applied Probability 24, no. 2 (June 1992): 455–73. http://dx.doi.org/10.2307/1427700.

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The distribution (1) used previously by the author to represent polymerisation of several types of unit also prescribes quite general statistics for a random field on a random graph. One has the integral expression (3) for its partition function, but the multiple complex form of the integral makes the nature of the expected saddlepoint evaluation in the thermodynamic limit unclear. It is shown in Section 4 that such an evaluation at a real positive saddlepoint holds, and subsidiary conditions narrowing down the choice of saddlepoint are deduced in Section 6. The analysis simplifies greatly in what is termed the semi-coupled case; see Sections 3, 5 and 7. In Section 8 the analysis is applied to an Ising model on a random graph of fixed degreer+ 1. The Curie point of this model is found to agree with that deduced by Spitzer for an Ising model on an r-branching tree. This agreement strengthens the conclusion of ‘locally tree-like' behaviour of the graph, seen as an important property in a number of contexts.
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Bender, E. A., and N. C. Wormald. "Random trees in random graphs." Proceedings of the American Mathematical Society 103, no. 1 (January 1, 1988): 314. http://dx.doi.org/10.1090/s0002-9939-1988-0938689-5.

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Whittle, P. "Random fields on random graphs." Advances in Applied Probability 24, no. 02 (June 1992): 455–73. http://dx.doi.org/10.1017/s0001867800047601.

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The distribution (1) used previously by the author to represent polymerisation of several types of unit also prescribes quite general statistics for a random field on a random graph. One has the integral expression (3) for its partition function, but the multiple complex form of the integral makes the nature of the expected saddlepoint evaluation in the thermodynamic limit unclear. It is shown in Section 4 that such an evaluation at a real positive saddlepoint holds, and subsidiary conditions narrowing down the choice of saddlepoint are deduced in Section 6. The analysis simplifies greatly in what is termed the semi-coupled case; see Sections 3, 5 and 7. In Section 8 the analysis is applied to an Ising model on a random graph of fixed degree r + 1. The Curie point of this model is found to agree with that deduced by Spitzer for an Ising model on an r-branching tree. This agreement strengthens the conclusion of ‘locally tree-like' behaviour of the graph, seen as an important property in a number of contexts.
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?uczak, Tomasz. "Random trees and random graphs." Random Structures and Algorithms 13, no. 3-4 (October 1998): 485–500. http://dx.doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<485::aid-rsa16>3.0.co;2-y.

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Dissertations / Theses on the topic "Random graphs"

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Ramos, Garrido Lander. "Graph enumeration and random graphs." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/405943.

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In this thesis we use analytic combinatorics to deal with two related problems: graph enumeration and random graphs from constrained classes of graphs. We are interested in drawing a general picture of some graph families by determining, first, how many elements are there of a given possible size (graph enumeration), and secondly, what is the typical behaviour of an element of fixed size chosen uniformly at random, when the size tends to infinity (random graphs). The problems concern graphs subject to global conditions, such as being planar and/or with restrictions on the degrees of the vertices. In Chapter 2 we analyse random planar graphs with minimum degree two and three. Using techniques from analytic combinatorics and the concepts of core and kernel of a graph, we obtain precise asymptotic estimates and analyse relevant parameters for random graphs, such as the number of edges or the size of the core, where we obtain Gaussian limit laws. More challenging is the extremal parameter equal to the size of the largest tree attached to the core. In this case we obtain a logarithmic estimate for the expected value together with a concentration result. In Chapter 3 we study the number of subgraphs isomorphic to a fixed graph in subcritical classes of graphs. We obtain Gaussian limit laws with linear expectation and variance when the fixed graph is 2-connected. The main tool is the analysis of infinite systems of equations by Drmota, Gittenberger and Morgenbesser, using the theory of compact operators. Computing the exact constants for the first estimates of the moments is in general out of reach. For the class of series-parallel graphs we are able to compute them in some particular interesting cases. In Chapter 4 we enumerate (arbitrary) graphs where the degree of every vertex belongs to a fixed subset of the natural numbers. In this case the associated generating functions are divergent and our analysis uses instead the so-called configuration model. We obtain precise asymptotic estimates for the number of graphs with given number of vertices and edges and subject to the degree restriction. Our results generalize widely previous special cases, such as d-regular graphs or graphs with minimum degree at least d.
En aquesta tesi utilitzem l'analítica combinatòria per treballar amb dos problemes relacionats: enumeració de grafs i grafs aleatoris de classes de grafs amb restriccions. En particular ens interessa esbossar un dibuix general de determinades famílies de grafs determinant, en primer lloc, quants grafs hi ha de cada mida possible (enumeració de grafs), i, en segon lloc, quin és el comportament típic d'un element de mida fixa triat a l'atzar uniformement, quan aquesta mida tendeix a infinit (grafs aleatoris). Els problemes en què treballem tracten amb grafs que satisfan condicions globals, com ara ésser planars, o bé tenir restriccions en el grau dels vèrtexs. En el Capítol 2 analitzem grafs planar aleatoris amb grau mínim dos i tres. Mitjançant tècniques de combinatòria analítica i els conceptes de nucli i kernel d'un graf, obtenim estimacions asimptòtiques precises i analitzem paràmetres rellevants de grafs aleatoris, com ara el nombre d'arestes o la mida del nucli, on obtenim lleis límit gaussianes. També treballem amb un paràmetre que suposa un repte més important: el paràmetre extremal que es correspon amb la mida de l'arbre més gran que penja del nucli. En aquest cas obtenim una estimació logarítmica per al seu valor esperat, juntament amb un resultat sobre la seva concentració. En el Capítol 3 estudiem el nombre de subgrafs isomorfs a un graf fix en classes de grafs subcrítiques. Quan el graf fix és biconnex, obtenim lleis límit gaussianes amb esperança i variància lineals. L'eina principal és l'anàlisi de sistemes infinits d'equacions donada per Drmota, Gittenberger i Morgenbesser, que utilitza la teoria d'operadors compactes. El càlcul de les constants exactes de la primera estimació dels moments en general es troba fora del nostre abast. Per a la classe de grafs sèrie-paral·lels podem calcular les constants en alguns casos particulars interessants. En el Capítol 4 enumerem grafs (arbitraris) el grau de cada vèrtex dels quals pertany a un subconjunt fix dels nombres naturals. En aquest cas les funcions generatrius associades són divergents i la nostra anàlisi utilitza l'anomenat model de configuració. El nostre resultat consisteix a obtenir estimacions asimptòtiques precises per al nombre de grafs amb un nombre de vèrtexs i arestes donat, amb la restricció dels graus. Aquest resultat generalitza àmpliament casos particulars existents, com ara grafs d-regulars, o grafs amb grau mínim com a mínim d.
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Seierstad, Taral Guldahl. "The phase transition in random graphs and random graph processes." Doctoral thesis, [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985760044.

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Engström, Stefan. "Random acyclicorientations of graphs." Thesis, KTH, Matematik (Avd.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-116500.

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Heckel, Annika. "Colourings of random graphs." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:79e14d55-0589-4e17-bbb5-a216d81b8875.

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We study graph parameters arising from different types of colourings of random graphs, defined broadly as an assignment of colours to either the vertices or the edges of a graph. The chromatic number X(G) of a graph is the minimum number of colours required for a vertex colouring where no two adjacent vertices are coloured the same. Determining the chromatic number is one of the classic challenges in random graph theory. In Chapter 3, we give new upper and lower bounds for the chromatic number of the dense random graph G(n,p)) where p ∈ (0,1) is constant. These bounds are the first to match up to an additive term of order o(1) in the denominator, and in particular, they determine the average colour class size in an optimal colouring up to an additive term of order o(1). In Chapter 4, we study a related graph parameter called the equitable chromatic number. This is defined as the minimum number of colours needed for a vertex colouring where no two adjacent vertices are coloured the same and, additionally, all colour classes are as equal in size as possible. We prove one point concentration of the equitable chromatic number of the dense random graph G(n,m) with m = pn(n-1)/2, p < 1-1/e2 constant, on a subsequence of the integers. We also show that whp, the dense random graph G(n,p) allows an almost equitable colouring with a near optimal number of colours. We call an edge colouring of a graph G a rainbow colouring if every pair of vertices is joined by a rainbow path, which is a path where no colour is repeated. The least number of colours where this is possible is called the rainbow connection number rc(G). Since its introduction in 2008 as a new way to quantify how well connected a given graph is, the rainbow connection number has attracted the attention of a great number of researchers. For any graph G, rc(G)≥diam(G), where diam(G) denotes the diameter. In Chapter 5, we will see that in the random graph G(n,p), rainbow connection number 2 is essentially equivalent to diameter 2. More specifically, we consider G ~ G(n,p) close to the diameter 2 threshold and show that whp rc(G) = diam(G) ∈ {2,3}. Furthermore, we show that in the random graph process, whp the hitting times of diameter 2 and of rainbow connection number 2 coincide. In Chapter 6, we investigate sharp thresholds for the property rc(G)≤=r where r is a fixed integer. The results of Chapter 6 imply that for r=2, the properties rc(G)≤=2 and diam(G)≤=2 share the same sharp threshold. For r≥3, the situation seems quite different. We propose an alternative threshold and prove that this is an upper bound for the sharp threshold for rc(G)≤=r where r≥3.
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Oosthuizen, Joubert. "Random walks on graphs." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86244.

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Thesis (MSc)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: We study random walks on nite graphs. The reader is introduced to general Markov chains before we move on more specifically to random walks on graphs. A random walk on a graph is just a Markov chain that is time-reversible. The main parameters we study are the hitting time, commute time and cover time. We nd novel formulas for the cover time of the subdivided star graph and broom graph before looking at the trees with extremal cover times. Lastly we look at a connection between random walks on graphs and electrical networks, where the hitting time between two vertices of a graph is expressed in terms of a weighted sum of e ective resistances. This expression in turn proves useful when we study the cover cost, a parameter related to the cover time.
AFRIKAANSE OPSOMMING: Ons bestudeer toevallige wandelings op eindige gra eke in hierdie tesis. Eers word algemene Markov kettings beskou voordat ons meer spesi ek aanbeweeg na toevallige wandelings op gra eke. 'n Toevallige wandeling is net 'n Markov ketting wat tyd herleibaar is. Die hoof paramaters wat ons bestudeer is die treftyd, pendeltyd en dektyd. Ons vind oorspronklike formules vir die dektyd van die verdeelde stergra ek sowel as die besemgra ek en kyk daarna na die twee bome met uiterste dektye. Laastens kyk ons na 'n verband tussen toevallige wandelings op gra eke en elektriese netwerke, waar die treftyd tussen twee punte op 'n gra ek uitgedruk word in terme van 'n geweegde som van e ektiewe weerstande. Hierdie uitdrukking is op sy beurt weer nuttig wanneer ons die dekkoste bestudeer, waar die dekkoste 'n paramater is wat verwant is aan die dektyd.
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Bienvenu, François. "Random graphs in evolution." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS180.

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Cette thèse est composée de cinq projets de recherche indépendants, tous en lien soit avec les graphes aléatoires, soit avec la biologie évolutive - mais pour la plupart à l'interface de ces deux disciplines. Dans les Chapitres 2 et 3, nous introduisons deux modèles de graphes aléatoires correspondant à la distribution stationnaire d'une chaîne de Markov. Le premier de ces modèles, que nous appelons le graphe "split-and-drift", décrit la structure et la dynamique des réseaux d'interfécondité; le second est une forêt aléatoire inspirée du modèle de Moran, modèle central de la génétique des populations. Le Chapitre 4 est consacré à l'étude d'une nouvelle classe de réseaux phylogénétiques basée sur les "tree-child networks", que nous appelons "ranked tree-child networks" (RTCNs). Nous expliquons comment les énumérer et les échantillonner, puis étudions la structure des grands RTCNs uniformes. Dans le Chapitre 5, nous prouvons un résultat général à propos de la percolation dans les graphes orientés aléatoirement : l'association positive du cluster de percolation orientée. Enfin, le Chapitre 6 traite d'une des statistiques les plus utilisées en biologie des population : l'âge moyen auquel les parents donnent naissance. Nous détaillons plusieurs problèmes liés à l'une des méthodes les plus utilisées pour le quantifier et proposons une méthode alternative
This thesis consists of five independent research projects, related either to random graphs or to evolutionary biology - and most often to both. Chapters 2 and 3 introduce two random graphs that are obtained as the stationary distributions of graph-valued Markov chains. The first of these, which we term the split-and-drift random graph, aims to describe the structure and dynamics of interbreeding-potential networks; the second one is a random forest that was inspired by the celebrated Moran model of population genetics. Chapter 4 is devoted to the study of a new class of phylogenetic networks that we term ranked tree-child networks, or RTCNs for short. These networks correspond to a subclass of tree-child networks that are endowed with an additional structure ensuring compatibility with a time-embedded evolutionary process, and are designed to model reticulated phylogenies. We focus on the enumeration and sampling of RTCNs before turning to the structural properties of large uniform RTCNs. In Chapter 5, we prove a general result about oriented percolation in randomly oriented graphs: the positive association of the percolation cluster. Finally, in Chapter 6 we focus on a widely used statistic of populations: the mean age at which parents give birth. We point out several problems with one of the most widely used way to compute it, and provide an alternative measure
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Johansson, Tony. "Random Graphs and Algorithms." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/938.

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This thesis is concerned with the study of random graphs and random algorithms. There are three overarching themes. One theme is sparse random graphs, i.e. random graphs in which the average degree is bounded with high probability. A second theme is that of finding spanning subsets such as spanning trees, perfect matchings and Hamilton cycles. A third theme is solving optimization problems on graphs with random edge costs.
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Ross, Christopher Jon. "Properties of Random Threshold and Bipartite Graphs." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306296991.

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Pymar, Richard James. "Random graphs and random transpositions on a circle." Thesis, University of Cambridge, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.610350.

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Crippa, Davide. "q-distributions and random graphs /." [S.l.] : [s.n.], 1994. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=10923.

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Books on the topic "Random graphs"

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Janson, Svante, Tomasz Łuczak, and Andrzej Rucinski. Random Graphs. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2000. http://dx.doi.org/10.1002/9781118032718.

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Kolchin, V. F. Random graphs. Cambridge, UK: Cambridge University Press, 1999.

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International Seminar on Random Graphs and Probabilistic Methods in Combinatorics. (2nd 1985 Uniwersytet im. Adama Mickiewicza w Poznaniu. Instytut Matematyki). Random graphs '85. New York: North-Holland, 1987.

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Chatterjee, Sourav. Large Deviations for Random Graphs. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65816-2.

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Ceccherini-Silberstein, Tullio, Maura Salvatori, and Ecaterina Sava-Huss, eds. Groups, Graphs and Random Walks. Cambridge: Cambridge University Press, 2017. http://dx.doi.org/10.1017/9781316576571.

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Palka, Zbigniew. Asymptotic properties of random graphs. Warszawa: Państwowe Wydawn. Nauk., 1988.

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Grimmett, Geoffrey. Probability on graphs: Random processes on graphs and lattices. Cambridge: Cambridge University Press, 2010.

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Marchette, David J. Random Graphs for Statistical Pattern Recognition. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2004. http://dx.doi.org/10.1002/047172209x.

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Spencer, Joel. The Strange Logic of Random Graphs. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04538-1.

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Spencer, Joel H. The strange logic of random graphs. Berlin: Springer, 2001.

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Book chapters on the topic "Random graphs"

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Bollobás, Béla. "Random Graphs." In Modern Graph Theory, 215–52. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0619-4_7.

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Brémaud, Pierre. "Random Graphs." In Discrete Probability Models and Methods, 255–86. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-43476-6_10.

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Diestel, Reinhard. "Random Graphs." In Graph Theory, 323–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-53622-3_11.

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Li, Xueliang, Colton Magnant, and Zhongmei Qin. "Random Graphs." In Properly Colored Connectivity of Graphs, 63–72. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89617-5_7.

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Bonato, Anthony, and Richard Nowakowski. "Random graphs." In The Student Mathematical Library, 133–64. Providence, Rhode Island: American Mathematical Society, 2011. http://dx.doi.org/10.1090/stml/061/06.

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Bonato, Anthony. "Random graphs." In Graduate Studies in Mathematics, 33–57. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/089/03.

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Diestel, Reinhard. "Random Graphs." In Graph Theory, 309–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-642-14279-6_11.

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Prömel, Hans Jürgen, and Anusch Taraz. "Random Graphs, Random Triangle-Free Graphs, and Random Partial Orders." In Computational Discrete Mathematics, 98–118. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45506-x_8.

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Gao, Pu, Mikhail Isaev, and Brendan D. McKay. "Sandwiching random regular graphs between binomial random graphs." In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 690–701. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611975994.42.

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Barthelemy, Marc. "Random Geometric Graphs." In Lecture Notes in Morphogenesis, 177–96. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-20565-6_9.

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Conference papers on the topic "Random graphs"

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Oren-Loberman, Mor, Vered Paslev, and Wasim Huleihel. "Testing Dependency of Weighted Random Graphs." In 2024 IEEE International Symposium on Information Theory (ISIT), 1263–68. IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619266.

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Frieze, Alan. "Random graphs." In the seventeenth annual ACM-SIAM symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1109557.1109663.

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Feng, Lijin, and Jackson Barr. "Complete Graphs and Bipartite Graphs in a Random Graph." In 2021 5th International Conference on Vision, Image and Signal Processing (ICVISP). IEEE, 2021. http://dx.doi.org/10.1109/icvisp54630.2021.00054.

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Mota, Guilherme Oliveira. "Advances in anti-Ramsey theory for random graphs." In II Encontro de Teoria da Computação. Sociedade Brasileira de Computação - SBC, 2017. http://dx.doi.org/10.5753/etc.2017.3204.

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Dados grafos G e H, denotamos a seguinte propriedade por G ÝrÑpb H: para toda coloração própria das arestas de G (com uma quantidade arbitrária de cores) existe uma cópia multicolorida de H em G, i.e., uma cópia de H sem duas arestas da mesma cor. Sabe-se que, para todo grafo H, a função limiar prHb prHbpnq para essa propriedade no grafo aleatório binomial Gpn; pq é assintoticamente no máximo n 1{mp2qpHq, onde mp2qpHq denota a assim chamada 2-densidade máxima de H. Neste trabalho discutimos esse e alguns resultados recentes no estudo de propriedades anti-Ramsey para grafos aleatórios, e mostramos que se H C4 ou H K4 então prHb n 1{mp2qpHq, que está em contraste com os fatos conhecidos de que prCbk n 1{mp2qpCkq para Let r be a positive integer and let G and H be graphs. We denote by G Ñ pHqr the property that any colouring of the edges of G with at most r colours contains a monochromatic copy of H in G. In 1995, Ro¨dl and Rucin´ski determined the threshold for the property Gpn; pq Ñ pHqr for all graphs H. The maximum 2-density mp2qpHq of a graph H is denoted by mp2qpHq max ! ||VEppJJqq|| 12 : J € H; |V pJ q| ¥ 3) ; where we suppose |V pHq| ¥ 3.
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Söderberg, B. "Random Feynman Graphs." In SCIENCE OF COMPLEX NETWORKS: From Biology to the Internet and WWW: CNET 2004. AIP, 2005. http://dx.doi.org/10.1063/1.1985383.

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Frieze, Alan, Santosh Vempala, and Juan Vera. "Logconcave random graphs." In the 40th annual ACM symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1374376.1374487.

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Zhao, Xiangyu, Hanzhou Wu, and Xinpeng Zhang. "Watermarking Graph Neural Networks by Random Graphs." In 2021 9th International Symposium on Digital Forensics and Security (ISDFS). IEEE, 2021. http://dx.doi.org/10.1109/isdfs52919.2021.9486352.

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Aiello, William, Fan Chung, and Linyuan Lu. "A random graph model for massive graphs." In the thirty-second annual ACM symposium. New York, New York, USA: ACM Press, 2000. http://dx.doi.org/10.1145/335305.335326.

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Servetto, Sergio D., and Guillermo Barrenechea. "Constrained random walks on random graphs." In the 1st ACM international workshop. New York, New York, USA: ACM Press, 2002. http://dx.doi.org/10.1145/570738.570741.

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Kim, Jeong Han, and Van H. Vu. "Generating random regular graphs." In the thirty-fifth ACM symposium. New York, New York, USA: ACM Press, 2003. http://dx.doi.org/10.1145/780542.780576.

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Reports on the topic "Random graphs"

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Mesbahi, Mehran. Dynamic Security and Robustness of Networked Systems: Random Graphs, Algebraic Graph Theory, and Control over Networks. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567125.

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Pawagi, Shaunak, and I. V. Ramakrishnan. Updating Properties of Directed Acyclic Graphs on a Parallel Random Access Machine. Fort Belvoir, VA: Defense Technical Information Center, September 1985. http://dx.doi.org/10.21236/ada162954.

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Moseman, Elizabeth. Improving the Computational Efficiency of the Blitzstein-Diaconis Algorithm for Generating Random Graphs of Prescribed Degree. National Institute of Standards and Technology, July 2015. http://dx.doi.org/10.6028/nist.ir.8066.

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Han, Guang, and Armand M. Makowski. A Strong Zero-One Law for Connectivity in One-Dimensional Geometric Random Graphs With Non-Vanishing Densities. Fort Belvoir, VA: Defense Technical Information Center, April 2007. http://dx.doi.org/10.21236/ada468079.

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Chandrasekhar, Arun, and Matthew Jackson. Tractable and Consistent Random Graph Models. Cambridge, MA: National Bureau of Economic Research, July 2014. http://dx.doi.org/10.3386/w20276.

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Carley, Kathleen M., and Eunice J. Kim. Random Graph Standard Network Metrics Distributions in ORA. Fort Belvoir, VA: Defense Technical Information Center, March 2008. http://dx.doi.org/10.21236/ada487516.

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Shue, Kelly, and Richard Townsend. How do Quasi-Random Option Grants Affect CEO Risk-Taking? Cambridge, MA: National Bureau of Economic Research, January 2017. http://dx.doi.org/10.3386/w23091.

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McCulloh, Ian, Joshua Lospinoso, and Kathleen M. Carley. The Link Probability Model: A Network Simulation Alternative to the Exponential Random Graph Model. Fort Belvoir, VA: Defense Technical Information Center, December 2010. http://dx.doi.org/10.21236/ada537329.

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Yoshida, Masami, Nammon Ruangrit, and Vorasuang Duangchinda. The application of exponential random graph models to online learning networks: a scoping review protocol. INPLASY - International Platform of Registered Systematic Review and Meta-analysis Protocols, July 2024. http://dx.doi.org/10.37766/inplasy2024.7.0039.

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Doerschuk, Peter C. University LDRD student progress report on descriptions and comparisons of brain microvasculature via random graph models. Office of Scientific and Technical Information (OSTI), October 2012. http://dx.doi.org/10.2172/1055646.

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