The Mixing Time of Glauber Dynamics for Colouring Regular Trees

Leslie Ann Goldberg; Mark Jerrum; Marek Karpinski

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arXiv · 0806.0921

The Mixing Time of Glauber Dynamics for Colouring Regular Trees

Leslie Ann Goldberg·Mark Jerrum·Marek Karpinski

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Abstract

We consider Metropolis Glauber dynamics for sampling proper $q$-colourings of the $n$-vertex complete $b$-ary tree when $3\leq q\leq b/2\ln(b)$. We give both upper and lower bounds on the mixing time. For fixed $q$ and $b$, our upper bound is $n^{O(b/\log b)}$ and our lower bound is $n^{Ω(b/q \log(b))}$, where the constants implicit in the $O()$ and $Ω()$ notation do not depend upon $n$, $q$ or $b$.

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BibTeX RIS

Leslie Ann Goldberg, Mark Jerrum, Marek Karpinski. 2008-06-05. The Mixing Time of Glauber Dynamics for Colouring Regular Trees. https://arxiv.org/abs/0806.0921

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