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Thresholds and the structure of sparse random graphs
Published 2003“…In this thesis, we obtain approximations to the non-3-colourability threshold of sparse random graphs and we investigate the structure of random graphs near the region where the transition from 3-colourability to non-3-colourability seems to occur. …”
Thesis -
42
The chromatic number of dense random graphs
Published 2018“…The chromatic number of the dense random graph G ∼ G(n, p) where p ∈ (0, 1) is constant has been intensively studied since the 1970s, and a landmark result by Bollob´as in 1987 first established the asymptotic value of χ(G) [4]. …”
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43
The phase transition in inhomogeneous random graphs
Published 2005“…We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. …”
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The continuum limit of critical random graphs
Published 2012“…We consider the Erdos-Rényi random graph G(n, p) inside the critical window, that is when p = 1/n + λn -4/3, for some fixed λ ε ℝ. …”
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46
The threshold for jigsaw percolation on random graphs
Published 2017“…In this note we determine the threshold for percolation up to a constant factor, in the case where both graphs are Erd˝os–R´enyi random graphs. …”
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47
Modularity of Erdos-Rényi random graphs
Published 2018“…For the Erdos-Rényi random graph Gn,pwith n vertices and edge-probability p, the likely modularity has three distinct phases. …”
Conference item -
48
Largest sparse subgraphs of random graphs
Published 2014“…For the Erdo{double acute}s-Rényi random graph G n,p, we give a precise asymptotic formula for the size α̂t(Gn,p) of a largest vertex subset in G n,p that induces a subgraph with average degree at most t, provided that p = p (n) is not too small and t = t (n) is not too large. …”
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49
The t-Improper Chromatic Number of Random Graphs
Published 2010“…We consider the t-improper chromatic number of the Erd′s-Rényi random graph Gn,p. The t-improper chromatic number χt(G) is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most t. …”
Journal article -
50
Clique colouring of binomial random graphs
Published 2018“…In this paper, we study the asymptotic behaviour of the clique chromatic number of the random graph G(n,p) for a wide range of edge-probabilities p=p(n). …”
Journal article -
51
The t-stability number of a random graph
Published 2008“…We investigate the typical values that this parameter takes on a random graph on n vertices and edge probability equal to p. …”
Journal article -
52
Dual-stage constructed random graph algorithm to generate random graphs featuring the same topological characteristics with power grids
Published 2017-09-01Subjects: Get full text
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53
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54
Generating Realistic Labelled, Weighted Random Graphs
Published 2015-12-01Subjects: Get full text
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55
Directed random graphs with given degree distributions
Published 2013-01-01Subjects: “…Directed random graphs…”
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56
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Ramsey Properties of Random Graphs and Folkman Numbers
Published 2017-08-01Subjects: Get full text
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58
Properties of Random Graphs via Boltzmann Samplers
Published 2007-01-01Subjects: “…random graphs with structural constraints…”
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59
Bergm: Bayesian Exponential Random Graphs in R
Published 2014-10-01“…In this paper we describe the main features of the Bergm package for the open-source R software which provides a comprehensive framework for Bayesian analysis of exponential random graph models: tools for parameter estimation, model selection and goodness-of- fit diagnostics. …”
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60
Rigorous Result for the CHKNS Random Graph Model
Published 2003-01-01Subjects: “…random graph…”
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Article