The Mixing Time of Glauber Dynamics for Colouring Regular Trees

Details The Mixing Time of Glauber Dynamics for Colouring Regular Trees The Mixing Time of Glauber Dynamics for Colouring Regular Trees

2008-06-05

arxiv.org/abs/0806.0921v1

Computer Science

Computational Complexity

Scientific paper

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 $n^{\Omega(b/q \log(b))}$, where the constants implicit in the $O()$ and $\Omega()$ notation do not depend upon $n$, $q$ or $b$.

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