FRACTIONAL k-FACTORS OF GRAPHS
图的分数κ-因子

Fractional graph theory is a new research subject in graph theory. Some results have been achieved concerning fractional matching, fractional coloring etc. Given a graph G = (V,E). Let a and b be two nonnegative integers. Let f: be a function. We call f a fractional a,b]-factor of G, if a b for all x V.A fractional k-factor f is a fractional a,b]-factor with a = b = k. In this article we give a necessary and sufficient condition for a graph to have a fractional k-factor with augmenting path method.