Hamilton-connectivity of 3-domination-critical graphs with α⩽δ Original Research Article

A graph G is 3-domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3-connected 3-domination critical graph with α(G)⩽δ(G). In this paper, we show that G is Hamilton-connected if and only if τ(G)>1, where τ(G) is the toughness of G.