Hamilton-connectivity of 3-domination critical graphs with α=δ+1≥5

Abstract

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-domination critical graph with toughness more than one. It was proved G is Hamilton-connected for the cases α ≤ δ (Discrete Mathematics 271 (2003) 1-12) and α=δ+2 (European Journal of Combinatorics 23(2002) 777-784). In this paper, we show G is Hamilton-connected for the case α= δ+1≥5.