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

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 that G is Hamilton-connected for the cases α ≤ δ [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with α ≤ δ, Discrete Math. 271 (2003) 1-12] and α = δ + 2 [Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with α = δ + 2, European J. Combin. 23 (2002) 777-784]. In this paper, we show G is Hamilton-connected for the case α = δ + 1 ≥ 5.