Deterministic counting of graph colourings using sequences of subgraphs

Clinical Orthopaedics and Related Research, Volume abs/0909.5, 2009.

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Keywords:
polynomial timediscrete mathematicsgibbs distributionrandom graph

Abstract:

In this paper we propose a deterministic algorithm for approximately counting the k-colourings of sparse random graphs G(n,d/n), (each edge is chosen independently with probability d/n and d is fixed). In particular, our algorithm computes in polynomial time a (1\pm n^(-Omega(1)))$-approximation of the logarithm of the number of k-colouri...More

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