图的分数κ-因子

FRACTIONAL k-FACTORS OF GRAPHS

给定图Ｇ＝（Ｖ，Ｅ）．设ａ和ｂ是两个非负整数．是一个函数．如果对所有的均成立，称 ｆ为 Ｇ的一个分数［ａ，ｂ］－ 因子． ａ＝ ｂ＝ κ时，称ｆ为 Ｇ的一个分数 ｋ＝因子．本文给出了一个图有分数 ｋ－因子的充分必要条件．

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.