| 边色临界图的1-因子和几乎1-因子的存在性 |
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| 引用本文： | 苗连英,杨星星,苗正科.边色临界图的1-因子和几乎1-因子的存在性[J].中国矿业大学学报,2010,39(2). |
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| 作者姓名： | 苗连英 杨星星 苗正科 |
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| 作者单位： | 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 |
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| 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.
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| 关 键 词： | 1-因子 几乎1-因子 边色数 临界图 |
On the Existence of 1-Factor and Almost 1-Factor of Edge Chromatic Critical Graphs |
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| MIAO Lian-ying,YANG Xing-xing,MIAO Zheng-ke.On the Existence of 1-Factor and Almost 1-Factor of Edge Chromatic Critical Graphs[J].Journal of China University of Mining & Technology,2010,39(2). |
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| Authors: | MIAO Lian-ying YANG Xing-xing MIAO Zheng-ke |
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| Affiliation: | MIAO Lian-ying1,YANG Xing-xing1,MIAO Zheng-ke2(1. School of Sciences,China University of Mining & Technology,Xuzhou,Jiangsu 221116,China,2. School of Mathematical Science,Xuzhou Normal University,China) |
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| Abstract: | Base on the Vizing's Adj acency 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. |
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| Keywords: | 1-factor almost 1-factor chromatic number critical graph |
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