图有分数因子的度条件

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{dG(u),dG(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 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.