分数n-可扩图的若干结果

Some Results of Fractional n-extendable Graphs

如果图G中有n-匹配并且对任意一个n-匹配M,G中都有一个分数完美匹配f使得对于任意e∈M,f(e)=1成立,那么G被称为是分数n-可扩图.马英红等首先引出此概念,并给出分数n-可扩图和极大分数n-可扩图的刻画.本文分别刻画了分数n-可扩二部图和极小分数n-可扩图,研究了k-因子临界图和分数n-可扩图之间的关系并利用图的bind-ing数和最小度给出了分数n-可扩图的两个充分条件.

A graph G is called fractional n-extendable if G has a n-matching and each n-matching M of G can be extended to a frac- tional perfect matching M of G such that f（e） = 1 for all e∈M. Ma and Liu firstly introduced the concept and characterized fractional n-extendable graphs and maximally fractional n-extendable graphs. In this paper, the author characterizes fractional n-extendable bi- partite graphs and minimally fractional n-extendable graphs, and studies the relation between fractional n-extendablegraphs and k-factor-critical graphs. In addition, the author gives two sufficient conditions of fractional n-extendable graphs in term of binding number and minimum degree respectively.