Matching and Factor-Critical Property in 3-Dominating-Critical Graphs∗
نویسندگان
چکیده
Let γ(G) be the domination number of a graphG. A graphG is dominationvertex-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 MSC: 05C69, 05C70
منابع مشابه
m at h . C O ] 2 8 A ug 2 00 6 Factor - Critical Property in 3 - Dominating - Critical Graphs ∗
A vertex subset S of a graph G is a dominating set if every vertex of G either belongs to S or is adjacent to a vertex of S. The cardinality of a smallest dominating set is called the dominating number of G and is denoted by γ(G). A graph G is said to be γ-vertex-critical if γ(G− v) < γ(G), for every vertex v in G. Let G be a 2-connected K1,5-free 3-vertex-critical graph. For any vertex v ∈ V (...
متن کامل. C O / 0 60 86 72 v 1 2 8 A ug 2 00 6 Factor - Critical Property in 3 - Dominating - Critical Graphs ∗
A vertex subset S of a graph G is a dominating set if every vertex of G either belongs to S or is adjacent to a vertex of S. The cardinality of a smallest dominating set is called the dominating number of G and is denoted by γ(G). A graph G is said to be γ-vertex-critical if γ(G− v) < γ(G), for every vertex v in G. Let G be a 2-connected K1,5-free 3-vertex-critical graph. For any vertex v ∈ V (...
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