Results 31 to 40 of about 2,603,262 (299)
Physical Review Letters, 2002 We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable.
R. MULET +3 more
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On the Vertex-Connectivity of an Uncertain Random Graph
IEEE Access, 2020 In many practical problems, randomness and uncertainty simultaneously appear in one complex system or network. When graph theory is applied to these problems, these complex systems or networks are usually represented by uncertain random graphs, in which ...
Hao Li, Xin Gao
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Random Graph Isomorphism [PDF]
SIAM Journal on Computing, 1980 A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i.e. all but $o(2^{( \begin{subarray}{l} n \\ 2 \end{subarray} )} )$) of the $2^{( \begin{subarray}{l} n \\ 2 \end{subarray} )} $ graphs on n vertices). Hence, for almost all graphs X, any graph Y can be easily tested for isomorphism to X by an extremely ...
László Babai +2 more
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Combinatorica, 1988 We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class.
Chung, F. R. K. +2 more
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Random rectangular graphs [PDF]
Physical Review E, 2015 A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides ...
Estrada, Ernesto, Sheerin, Matthew
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Universality of Random Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2012 We prove that asymptotically (as $n\to\infty$) almost all graphs with n vertices and $C_dn^{2-\frac{1}{2d}} \log^{\frac{1}{d}} n$ edges are universal with respect to the family of all graphs with maximum degree bounded by d. Moreover, we provide an efficient deterministic embedding algorithm for finding copies of bounded degree graphs in graphs ...
Domingos Dellamonica Jr. +3 more
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Scaling limit for the random walk on the largest connected component of the critical random graph [PDF]
, 2012 In this article, a scaling limit for the simple random walk on the largest connected component of the Erdos-Rényi random graph G(n,p) in the critical window, p = n−1+λn−4/3, is deduced.
Croydon, David A.
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Random matrices and random graphs
ESAIM: Proceedings and Surveys, 2023 We collect recent results on random matrices and random graphs. The topics covered are: fluctuations of the empirical measure of random matrices, finite-size effects of algorithms involving random matrices, characteristic polynomial of sparse matrices and Voronoi tesselations of split trees.
Capitaine Mireille +4 more
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A Probabilistic Counting Lemma for Complete Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We prove the existence of many complete graphs in almost all sufficiently dense partitions obtained by an application of Szemerédi's Regularity Lemma.
Stefanie Gerke +2 more
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Finding planted partitions in random graphs with general degree distributions [PDF]
, 2009 We consider the problem of recovering a planted partition such as a coloring, a small bisection, or a large cut in an (apart from that) random graph. In the last 30 years many algorithms for this problem have been developed that work provably well on ...
Coja-Oghlan, Amin +3 more
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