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APPROX
2015
Springer

Local Convergence of Random Graph Colorings

5 years 7 months ago
Local Convergence of Random Graph Colorings
Let G = G(n, m) be a random graph whose average degree d = 2m/n is below the k-colorability threshold. If we sample a k-coloring σ of G uniformly at random, what can we say about the correlations between the colors assigned to vertices that are far apart? According to a prediction from statistical physics, for average degrees below the so-called condensation threshold dk,cond, the colors assigned to far away vertices are asymptotically independent [Krzakala et al: PNAS 2007]. We prove this conjecture for k exceeding a certain constant k0. More generally, we determine the joint distribution of the k-colorings that σ induces locally on the bounded-depth neighborhoods of a fixed number of vertices. 1998 ACM Subject Classification G.2 Discrete Mathematics, G.3 Probability and Statistics, G.2.2. Graph Theory, F.2.2, Computations on discrete structures Keywords and phrases Random graph, Galton-Watson tree, phase transitions, graph coloring, Gibbs distribution, convergence Digital Object...
Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari
Added 16 Apr 2016
Updated 16 Apr 2016
Type Journal
Year 2015
Where APPROX
Authors Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari
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