关于图的分数k-可扩性的若干结果(英文)

Some Results on Fractional k-extendable Graphs

一个图称为是分数k-可扩的,若图G含有k条边的对集且对图G的任意一个k条边的对集M,都存在G的一个分数1-因子G_h,使得对任意的e∈M有h(e)=1。我们研究了分数k-可扩图的特征,给出了带有某些约束的分数k-可扩图存在充分条件,以及极大分数k-可扩图的特征。

A graph G is called a fractional k-extendable if it has a k-matching and every k-matching M of G is contained in a fractional l-frctor G_h of G such that h(e)=1 for all e∈M. In this paper, the characterization of fractional k-extendable graphs is discussed, some sufficient conditions for graphs to be fractional k-extendable are given. Furthermore, the characterization of a maximal fractional k-extendable graph is repersented.