Randomly colouring graphs with girth five and large maximum degree

Authors:
Lap Chi Lau;Michael Molloy
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario, Canada;Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
Venue:
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Year:
2006

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Abstract

We prove that the Glauber dynamics on the k-colourings of a graph G on n vertices with girth 5 and maximum degree Δ≥1000 log3n mixes rapidly if k=qΔ and qβ where β=1.645... is the root of 2-(1-e−1/β)2−2βe−1/β = 0.