图有分数因子的度条件(英文)  

A Degree Condition for Graphs to Have Fractional Factors

作　　者：禹继国[1] 刘桂真[2] 马美杰[3] 曹宝香[1] 

机构地区：[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

出　　处：《数学进展》2006年第5期621-628,共8页Advances in Mathematics（China）

基　　金：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。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 κ≥ 1, and let G be a connected graph of order n with n ≥ 4κ - 3, and minimum degree 5（G）≥κ. 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 κ-factor. Furthermore, we prove that the result is the best possible in some sense.

关 键 词：度条件 因子 分数κ-因子 

分 类 号：O157.5[理学—数学]