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

作　　者：黄晓娴[1] 刘岩[1] 吴博思 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《运筹学学报》2016年第1期125-130,共6页Operations Research Transactions

基　　金：国家自然科学基金(No.11551003);广州市科技计划项目科学研究专项基金(No.201510010265)

摘　　要：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.

关 键 词：分数完美匹配 分数k-因子临界的 分数k-可扩的 分数匹配数 

分 类 号：O157.5[理学—数学]