Results for random graphs
Treewidth of Erdős–Rényi random graphs, random intersection graphs, and scale-free random graphs
... Erdős–Rényi random graph has treewidth at most 2 if the edge- to-vertex ratio is less than 1 / 2, completely settles the exact threshold of the edge-to-vertex ratio for the property of having a linear treewidth in ...
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Convergence of Random Graphs
... 1 Random graphs in local topology This section is mainly dedicated to give to the reader a general view on random pointed ...some results on random pointed graphs from the local ...
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PERCOLATION AND RANDOM GRAPHS
... 1.1 Introduction and notation In this section, we discuss random networks. In Section 1.2, we study perco- lation, which is obtained by independently removing vertices or edges from a graph. Percolation is a model ...
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Sampling random colorings of sparse random graphs
... Sampling Random Colorings of Sparse Random Graphs ∗ Charilaos Efthymiou † Thomas ...sparse random graph G(n, d/n) for constant ...mixing results for general graphs are in terms ...
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On the KŁR conjecture in random graphs
... extremal results about graphs to subgraphs of the random graph G n,p , including Ramsey’s theorem [67] and the Erd˝os-Simonovits stability theorem ...sparse random versions do not follow from ...
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Threshold phenomena in random graphs
... 1950s, random graphs appeared for the first time in a result of the prolific hungarian mathematician Pál ...in random graph theory has only grown up until ...Web, random graphs are even ...
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Geometric Inhomogeneous Random Graphs
... our results in this paper crucially depend on an underlying geometry, and thus do not hold in the more general model from [14] where no underlying geometry is ...a random graph from a fixed distribution, ...
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Universality of Cutoff for Random Walks on Random Cayley Graphs
... our results into a broader ...include random birth and death chains [31, 72], the simple or non-backtracking RW on various models of sparse random graphs, including random regular ...
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Cliques in dense in homogeneous random graphs
... 2. OUR CONTRIBUTION In this section we present our main results. The notation in this section is standard. We refer the reader to Section 3 for formal definitions. We saw that for many natural graphons W , ω( G ...
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Approximating layout problems on random graphs
... for random graphs drawn from the G(n; p n ) model where C=n6p n 61 for all n bigenough and for some properly characterized parameter C ¿ ...our results establish that, with overwhelmingprobability, ...
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Clique coloring of binomial random graphs
... holds tends to 1 as n goes to infinity. Since we aim for results that hold whp, we will always assume that n is large enough. We often write G(n, p) when we mean a graph drawn from the distribution G(n, p). ...
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Chromatic thresholds in sparse random graphs
... 3-chromatic graphs H for which δ χ (H, p) = 0 are exactly the ‘thundercloud-forest graphs’, see Defini- tion ...the results of this paper and those in [1], this conjecture (if true) would completely ...
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Two Basic Results Concerning Random Walks on Graphs »
... Suppose now that G is a finite graph. The question of hitting probabilities of points can be handled in a similar way to the above argument, where we still must look for harmonic functions on the graph. However, there is ...
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Random rectangular graphs
... 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 random ...
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Random rectangular graphs
... consider graphs with n = 100 nodes and the extreme cases a = 1 (RGG) and a = 30 ...the results for both cases are very similar and they are characterized by an abrupt increase in the clustering at the ...
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Synchronizability of random rectangular graphs
... the random geometric graph (RGG) model, which is formu- lated over a cubic region in ...developed random rectangular graph (RRG) model, in which the spatial domain of the net- works is a rectangle that ...
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On the diameter of random planar graphs
... The results for planar graphs contrast with the so-called “subcritical” graph families, such as trees, outerplanar graphs, and series-parallel graphs, where the diameter is in the interval (n ...
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On the diameter of random planar graphs
... a random connected planar graph rescaled by n 1/4 ; in- stead we have obtained large deviation results on the diameter that strongly support the belief that n 1/4 is the right scaling ...
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Synchronizability of random rectangular graphs
... the random geometric graph (RGG) model, which is formu- lated over a cubic region in ...developed random rectangular graph (RRG) model, in which the spatial domain of the net- works is a rectangle that ...
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Epidemics on random intersection graphs
... on results for the final outcome of homogeneously mixing SIR epidemic .... Results for homogeneously mixing SIR epidemic models are outlined in Section ...
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