中文

Operations Research Transactions ›› 2016, Vol. 20 ›› Issue (1): 125-130.doi: 10.15960/j.cnki.issn.1007-6093.2016.01.013

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

HUANG Xiaoxian1  LIU Yan1,*  WU Bosi1   

  1. 1.  School of Mathematical Science, South China Normal University, Guangzhou 510631, China
  • Received:2015-05-28 Online:2016-03-15 Published:2016-03-15

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Abstract:

 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 k-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.

Key words: fractional perfect matching, fractional k-factor-critical, fractional k-extendable, fractional matching number