On the Existence of 1-Factor and Almost 1-Factor of Edge Chromatic Critical Graphs
Zhengke Miao · Journal of China University of Mining and Technology · 2010
Base on the Vizing's Adjacency Lemma,three results on critical graphs and bipartite graphs,and the necessary and sufficient conditions about the existence of 1-factor and almost 1-factor of graphs,the following results are proved by the method of structural graph theory in this paper:1) G has a 1-factor if G is a critical graph of order 2n,and δ(G)≥n-3; 2) G has a almost 1-factor if G is a critical graph of order 2n+1,and δ(G)≥n-4.