Bounds on connective constants of regular graphs

Abstract

Bounds are proved for the connective constant μ of an infinite, connected, Δ-regular graph G. The main result is that μ \ge \sqrt{Δ-1} if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.

v2: small fix applied to Thm 3.2

References in corpus (3)

• Lectures on Self-Avoiding Walks
• Non-coincidence of Quenched and Annealed Connective Constants on the supercritical planar percolation cluster
• Self-avoiding walks and the Fisher transformation

Cited by in corpus (1)

• Existence of a non-averaging regime for the self-avoiding walk on a high-dimensional infinite percolation cluster