Sampling Edge Covers in 3-Regular Graphs

An edge cover 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 oil 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.