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