一类特殊图的独立数和f-因子存在性的关系

The Independent Number of a Specified Graph and the Existence of f-factor

设G是一个图,f是定义在V(G)上的一个非负整数值函数。如果图G的一个支撑子F满足对任意的x∈V(F)都有dF(x)=f(x),则称F为图G的一个f-因子。本文在一类特殊图中给出了图的独立数和f-因子存在性的关系。

Let G be a graph with vertex set V（G）and let { be a nonnegative integer--valued function defined on V（G）. A spanning subgraph F of G is called an f- factor if dF（x）=f（x）for every. In this paper we present some sufficient conditions for the existence of f-factors and connected （f-2, f）-- factors in K1, n--free graphs. The conditions involve the minimum degree, the stability number and the connectivity of graph G.