Hamilton-connectivity of 3-Domination Critical Graphs with α = δ + 2

A graph G is 3-domination critical if its domination number \gamma is 3 and the addition of any edge decreases \gamma by 1. It was proved by Favaron et al. that α ≤ δ + 2 for any connected 3-domination critical graph. Denote byτ (G) the toughness of a graph G. Recently Chen et al. conjectured that a connected 3-domination critical graph G is Hamilton-connected if and only if τ(G) > 1 and showed the conjecture is true when α ≤ δ. In this paper, by using a closure operation defined by Bondy and Chvátal, we show the conjecture is true whenα = δ + 2.