| 图存在分数［a,b］-因子的一个孤立韧度条件 |
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| 引用本文： | 潘瑞霞,兰梅,刘桂真. 图存在分数［a,b］-因子的一个孤立韧度条件[J]. 山东大学学报(理学版), 2008, 43(5): 93-96 |
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| 作者姓名： | 潘瑞霞 兰梅 刘桂真 |
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| 作者单位： | 1. 山东大学数学学院,山东,济南,250100
2. 济南职业学院财经系,山东,济南,250103 |
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| 摘 要： | 给出了图的孤立韧度I(G)与分数［a,b］-因子存在性间的关系，证明了若δ(G)≥I(G)≥a-1+(a-1)／b,其中a、b均为整数,2≤a＜b,则图G有分数［a,b］-因子。进一步证明该结论在一定意义下是最好的，并且提出猜想当a=b时结论仍然成立。
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| 关 键 词： | 图 孤立韧度 分数［a,b］-因子 |
| 文章编号： | 1671-9352(2008)05-0093-04 |
| 修稿时间： | 2007-12-28 |
A condition of isolated toughness on the existence of fractional [a,b]-factors of graphs |
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| PAN Rui-xia,LAN Mei,LIU Gui-zhen. A condition of isolated toughness on the existence of fractional [a,b]-factors of graphs[J]. Journal of Shandong University, 2008, 43(5): 93-96 |
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| Authors: | PAN Rui-xia LAN Mei LIU Gui-zhen |
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| Affiliation: | 1. School of Mathematics and System Science, Shandong University, Jinan 250100, Shandong, China;2. Department of Finance and Economics, Jinan Training College, Jinan 250103, Shandong, China |
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| Abstract: | The relationships between the isolated toughness I(G) and the existence of fractional ［a,b］-factors were given. It was proved thatif δ(G)≥I(G)≥a-1+(a-1)／b, then G has a fractional ［a,b］-factor where 2≤a＜b. The results are best possible in some sense. In addition a conjecture about a=b was given. |
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| Keywords: | graph isolated toughness fractional ［a,b］-factors |
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