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| 图有分数因子的度条件 | |
| 引用本文： | 禹继国,刘桂真,马美杰,曹宝香.图有分数因子的度条件[J].数学进展,2006,35(5):621-628. |
| 作者姓名： | 禹继国 刘桂真 马美杰 曹宝香 |
| 作者单位： | 1. 曲阜师范大学计算机科学学院,日照,山东,276826 2. 山东大学数学与系统科学学院,济南,山东,250100 3. 中国科技大学数学系,合肥,安徽,230026 |
| 基金项目： | The work is supported by NSFC(No.10471078),RFDP(No.20040422004) of Higher Education,Promotional Foundation (2005BS01016) for Mid-aged for Young Scientists of Shangdong Province,DRF of QFNU and NSF(Y2003G01) of Shandong Province. |
| 摘 要： | 本文研究了图有分数因子的度条件,得到了下面的结果：令k(?)1是一个整数,G是一个连通的n阶图,n(?)4k-3且最小度δ(G)(?)k,若对于每一对不相邻的顶点u,v∈V(G)都有max{d_G(u),d_G(v)}(?)n/2,则G有分数k-因子．并指出该结果在一定意义上是最好可能的。 |
| 关 键 词： | 度条件 因子 分数 k-因子 |
| 文章编号： | 1000-0917（2006）05-0621-08 |
| 收稿时间： | 2004-11-01 |
| 修稿时间： | 2005-07-25 |
A Degree Condition for Graphs to Have Fractional Factors |
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| YU Ji-guo,LIU Gui-zhen,MA Mei-jie,CAO Bao-xiang.A Degree Condition for Graphs to Have Fractional Factors[J].Advances in Mathematics,2006,35(5):621-628. | |
| Authors: | YU Ji-guo LIU Gui-zhen MA Mei-jie CAO Bao-xiang |
| Institution: | 1. School of Computer Science, Qufu Normal Univ., Rizhao, Shandong, 276826, P. R. China; 2. School of Math. and System Science, Shandong Univ., Jinan, Shandong, 250100, P. R. China; 3. Dept. of Math., Univ. of Science and Technology of China, Hefei, Anhui, 230026, P. R. China |
| Abstract: | In this paper, a degree condition for a graph to have fractional factors is studied. The following result is obtained. Let k be an integer such that k ≥ 1, and let G be a connected graph of order n with n ≥ 4k - 3, and minimum degree δ(G) ≥ k. If G satisfies max{(dG(u),dG(v)} ≥ n/2 for each pair of nonadjacent vertices u,v ∈ V(G), then G has a fractional k-factor. Furthermore, we prove that the result is the best possible in some sense. |
| Keywords: | degree condition factor fractional k-factor |
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