Abstract
AbstractWe study the Glauber dynamics Markov chain for k-colourings of trees with maximum degree Δ. For k ≥ 3, we show that the mixing time on every tree is at most n O(1 + Δ/(k logΔ)). This bound is tight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses a weighted canonical paths analysis and a variation of the block dynamics that exploits the differing relaxation times of blocks.KeywordsPlanar GraphMaximum DegreeBoundary NodeGlauber DynamicProper ColouringThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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