The Mixing Time of Glauber Dynamics for Colouring Regular Trees

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 n(b/q log(b)), where the constants implicit in the O() and () notation do not depend upon n, q or b.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Leslie Ann Goldberg, Mark Jerrum, Marek Karpinski
• Keywords: Complete B-ary Tree, CORR 2008, Education, Lower Bound, Metropolis Glauber