The Mixing Time of Glauber Dynamics for Colouring Regular Trees

@article{Goldberg2010TheMT,
  title={The Mixing Time of Glauber Dynamics for Colouring Regular Trees},
  author={Leslie Ann Goldberg and Mark Jerrum and Marek Karpinski},
  journal={Random Struct. Algorithms},
  year={2010},
  volume={36},
  pages={464-476}
}
We consider Metropolis Glauber dynamics for sampling proper qcolourings of the n-vertex complete b-ary tree when 3 ≤ q ≤ b/2 ln(b). We give both upper and lower bounds on the mixing time. For fixed q and b, our upper bound is nO(b/ log b) and our lower bound is nΩ(b/q log(b)), where the constants implicit in the O() and Ω() notation do not depend upon n, q or b. 

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