Matching and factorcritical property in 3-domination-critical graphs

Abstract

Let y(G) be the domination number of a graph G. A graph G is dominationvertex-critical, or γ-vertex-critical, if γ(G - v) < y(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 K_1,6-free, then G has a perfect matching; (2) If G is of odd order and K₁₇-free, then G has a near perfect matching with only three exceptions. All these results improve the known results.