### The Mixing Time of Glauber Dynamics for Colouring Regular TreesThe Mixing Time of Glauber Dynamics for Colouring Regular Trees

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 Author Goldberg, Leslie Ann ♦ Jerrum, Mark ♦ Karpinski, Marek Source arXiv.org Content type Text File Format PDF Date of Submission 2008-06-05 Language English
 Subject Domain (in DDC) Computer science, information & general works Subject Keyword Computer Science - Computational Complexity ♦ Computer Science - Discrete Mathematics ♦ cs 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 $n^{\Omega(b/q \log(b))}$, where the constants implicit in the $O()$ and $\Omega()$ notation do not depend upon $n$, $q$ or $b$. Educational Use Research Learning Resource Type Article