| 图的分数因子与孤立韧度 |
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| 引用本文： | 马英红,刘桂真.图的分数因子与孤立韧度[J].应用数学,2006,19(1):188-194. |
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| 作者姓名： | 马英红 刘桂真 |
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| 作者单位： | 1. 山东师范大学管理学院,山东,济南,250014
2. 山东大学系统科学学院,山东,济南,250100 |
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| 摘 要： | 图G的孤立韧度定义为I(G)=min{｜S｜/i(G-S)∶SV(G),i(G-S)≥2},若G不是完全图.否则令I(G)=∞.本文给出了图的分数k因子与图的分数a,b]因子的存在性与图的孤立韧度的关系.证明了,若δ(G)≥k且I(G)≥k,则G有分数k因子;若δ(G)≥I(G)≥a-1 a/b,则图G有分数a,b]因子,其中a
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| 关 键 词： | 图 分数因子 孤立韧度 |
| 文章编号： | 1001-9847(2006)01-0188-07 |
| 收稿时间： | 2005-04-30 |
| 修稿时间： | 2005年4月30日 |
Fractional Factors and Isolated Toughness of Graphs |
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| MA Ying-hong,LIU Gui-zhen.Fractional Factors and Isolated Toughness of Graphs[J].Mathematica Applicata,2006,19(1):188-194. |
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| Authors: | MA Ying-hong LIU Gui-zhen |
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| Institution: | 1. School of Management, Shanclong Normal University, Jinan 250014, China ; 2. School of Mathematics and System Science, Shandong University, Jinan 250100, China |
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| Abstract: | The isolated toughness of G is defined as I(G) = min{|S|/i(G- S): S (∪_)V(G),i(GS) ≥ 2} if G is not complete. Otherwise, set I(G) = ∞. In this paper, the relationships between the isolated toughness and the existence of fractional k- factors and fractional a,b]- factors are given. It is proved that if δ(G) ≥ k and I(G) ≥k, thenGhas a fractionalk- factor;ifδ(G) ≥ I(G) ≥ a- 1+a/b, then G has a fractional a,b]- factor where a ＜ b. Furthermore, it is showed that the results in this paper are best possible in some sense. |
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| Keywords: | Graph Fractional factor Isolated toughness |
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