A conjecture on 3-vertex-critical graphs
HuiQing LIU, Mei Lu, Shunzhe Zhang · Scientia Sinica Mathematica · 2013
Let γ(G) be the domination number of a graph G. A graph G is γ-vertex-critical if γ(G-v) < γ(G) for every vertex v ∈ V (G). In this paper, we show that if G is a 3-vertex-critical graph of even order n ≥ 18 and K1,7-free, then G contains a perfect matching with some exceptions. Our result solves a conjecture proposed by Ananchuen and Plummer.