Sampling edge covers in 3-regular graphs

Abstract

An edge cover C of an undirected graph is a set of edges such that every vertex has an adjacent edge in C. We show that a Glauber dynamics Markov chain for edge covers mixes rapidly for graphs with degrees at most three. Glauber dynamics have been studied extensively in the statistical physics community, with special emphasis on lattice graphs. Our results apply, for example, to the hexagonal lattice. Our proof of rapid mixing introduces a new cycle/path decomposition for the canonical flow argument. © 2009 Springer Berlin Heidelberg.