关于分数k-因子临界图与分数k-可扩图的若干结果

Some results on fractional k-factor-critical graphs and fractional k-extendable graphs

一个简单图G,如果对于V(G)的任意k元子集S,子图G-S都包含分数完美匹配,那么称G为分数后-因子临界图.如果图G的每个k-匹配M都包含在一个分数完美匹配中,那么称图G为分数k-可扩图.给出一个图是分数k-因子临界图和分数k-可扩图的充分条件,并给出一个图是分数k-因子临界图的充分必要条件.

A simple graph G is said to be fractional k-factor-critical if after deleting any k vertices,the remaining subgraph still has a fractional perfect matching.A graph G is called a fractional k-extendable graph if G has a fractional perfect matching containing M for any fc-matching M.In this paper,a sufficient condition for a graph to be fractional k-factor-critical graph and fractional k-extendable graph is given,respectively.Besides,a sufficient and necessary condition for a graph to be fractional k-factor-critical graph is given.