Factor-critical property in 3-dominating-critical graphs

Let γ(G) be the domination number of a graph G. A graph G is domination-vertex-critical, or γ-vertex-critical, if γ(G− v) < γ(G) for every vertex v ∈ V (G). In this paper, we show that: Let G be a γ-vertex-critical graph and γ(G) = 3. (1) If G is of even order and K1,6-free, then G has a perfect matching; (2) If G is of odd order and K1,7-free, then G has a near perfect matching with only three exceptions. All these results improve the known results. Keyword : Vertex coloring, domination number, 3-γ-vertex-critical, matching, near perfect matching, bicritical