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

A graph G   is 3-domination critical if its domination number γγ is 3 and the addition of any edge decreases γγ 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⩽δα⩽δ [Y.J. Chen, F. Tian, B. Wei, Hamilton-connectivity of 3-domination critical graphs with α⩽δα⩽δ, Discrete Math. 271 (2003) 1–12] and α=δ+2α=δ+2 [Y.J. Chen, F. Tian, Y.Q. Zhang, Hamilton-connectivity of 3-domination critical graphs with α=δ+2α=δ+2, European J. Combin. 23 (2002) 777–784]. In this paper, we show G   is Hamilton-connected for the case α=δ+1⩾5α=δ+1⩾5.