Existence of 1-Factor and Almost 1-Factor of Edge Chromatic Critical Graphs
QU Ji-bin · Journal of China University of Mining and Technology · 2008
Based on the Vizing's Adjacency Lemma,a result about the independent number of critical 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: 1) G has a 1-factor if G is a Δ-critical graph of order 2n,Δ≥n,and δ≥n-2;2) G has an almost 1-factor if G is a Δ-critical graph of order 2n+1,Δ≥n+1 and δ≥n-2.