The Glauber Dynamics for Colourings of Bounded Degree Trees

We study the Glauber dynamics Markov chain for k-colourings of trees with maximum degree ∆.For k ≥ 3, we show that the mixing time on every tree is at most n . This bound istight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses aweighted canonical paths analysis and a variation of the block dynamics in which we exploit the differingrelaxation times of blocks. Dept of Computer Science, University of Toronto, [email protected] of Computer Science, University of Toronto, [email protected] Research, [email protected].