边色临界图的1-因子和几乎1-因子的存在性  

On the Existence of 1-Factor and Almost 1-Factor of Edge Chromatic Critical Graphs

作　　者：苗连英[1] 杨星星[1] 苗正科[2] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116 [2]徐州师范大学数学系,江苏徐州221116

出　　处：《中国矿业大学学报》2010年第2期302-306,共5页Journal of China University of Mining & Technology

基　　金：国家自然科学基金项目(10871166)

摘　　要：根据Vizing邻接引理和关于临界图和二分图的3个结论,利用图的1-因子和几乎1-因子存在的充要条件,采用结构图论的方法证明了:1)若G是2n阶临界图,且δ(G)≥n-3,则G存在1-因子;2)若G是2n+1阶临界图,且δ(G)≥n-4,则G存在几乎1-因子.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.

关 键 词：1-因子 几乎1-因子 边色数 临界图 

分 类 号：O157.5[理学—数学]