随机上色图形与下界的周长和最大程度

Proceedings 2001 IEEE International Conference on Cluster Computing Pub Date : 2001-10-14 DOI:10.1109/SFCS.2001.959934

M. Dyer, A. Frieze

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引用次数: 72

摘要

我们考虑生成图G=(V, E)的随机q-着色问题。我们考虑简单的Glauber动力学链。我们证明，如果最大度/spl δ />c/sub - 1/ ln n和周长g>c/sub - 2/ ln - ln n (n=|V|)，则在c/sub - 1/、c/sub - 2/足够大的情况下，q/A>/spl β /，其中/spl β //spl ap/1.763是/spl β /=e/sup 1//spl β //的根。对于这类图，这优于E. Vigoda(1999)对于一般图的11/spl Delta//6界。我们将结果推广到随机图。

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Randomly colouring graphs with lower bounds on girth and maximum degree

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 /spl Delta/>c/sub l/ ln n and the girth g>c/sub 2/ ln ln n (n=|V|), then this chain mixes rapidly provided C/sub 1/, C/sub 2/ are sufficiently large, q/A>/spl beta/, where /spl beta//spl ap/1.763 is the root of /spl beta/=e/sup 1//spl beta//. For this class of graphs, this beats the 11/spl Delta//6 bound of E. Vigoda (1999) for general graphs. We extend the result to random graphs.

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Proceedings 2001 IEEE International Conference on Cluster Computing

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