The Glauber dynamics on colourings of a graph with high girth and maximum degree
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
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IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We consider the problem of generating a random q-colouring of a graph G = (V;E). We consider the simple Glauber Dynamics chain. We show that if the maximum degree \delta c1 ln n and the girth g c2 ln ln n (n = |V|) then this chain mixes rapidly provided c1, c2 are sufficiently large, {q \mathord{\left/ {\vphantom {q {\Delta \beta }}} \right. \kern-\nulldelimiterspace} {\Delta