Toughness and binding number

Abstract

Let τ(G) and bind(G) be the toughness and binding number, respectively, of a graph G. Woodall observed in 1973 that τ(G)≥bind(G)-1. In this paper, we obtain best possible improvements of this inequality except when (1+5)/2 <2 and bind(G) has even denominator when expressed in lowest terms. © 2013 Elsevier B.V. All rights reserved.