Abstract
We study the Glauber dynamics Markov chain for k-colorings of trees with maximum degree Δ. For k≥3, we show that the mixing time on the complete tree is nθ(1+Δ/(klogΔ)). For k≥4 we extend our analysis to show that the mixing time on any tree is at most nO(1+Δ/(klogΔ)). Our proof uses a weighted canonical paths analysis and introduces a variation of the block dynamics that exploits the differing relaxation times of blocks.
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