Randomly coloring graphs of bounded treewidth

We consider the problem of sampling a proper $k$-coloring of a graph of maximal degree $\mathrm{\Delta }$ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of bounded treewidth if $k\ge (1+ϵ)\mathrm{\Delta }$, for any $ϵ>0$.