We consider the problem of sampling a proper k-coloring of a graph of maximal degree ∆ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of logarithmically bounded pathwidth if k ≥ (1 + )∆, for any > 0, using a hybrid paths argument. ACM Subject Classification Theory of computation → Random walks and Markov chains, Mathematics of computing → Markov-chain Monte Carlo methods Keywords and phrases Random coloring, Glauber dynamics,

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... Markov-chain Monte Carlo Digital Object Identifier 10.4230/LIPIcs.APPROX-RANDOM.2018.57 Related Version A full version of the paper is available at https://hal.archives-ouvertes. fr/hal-01832102. 1 Supported in part by the Linde Foundation and NSF grants CNS-1254169 and CNS-1518941. 2 We define precisely what we mean by "almost" in Section 2.2.