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math.CO2013★ 6 cited
On the chromatic number of random regular graphs
Amin Coja-Oghlan, Charilaos Efthymiou, Samuel Hetterich
Let G(n,d) be the random d-regular graph on n vertices. For any integer k exceeding a certain constant k_0 we identify a number d_{k-col} such that G(n,d) is k-colorable w.h.p. if…
cs.DM2013★ 5 cited
MCMC sampling colourings and independent sets of G(n,d/n) near the uniqueness threshold
Charilaos Efthymiou
Sampling from Gibbs distribution is a central problem in computer science as well as in statistical physics. In this work we focus on the k-colouring model} and the hard-core model…