偶图的分数因子

Fractional Factors of Bipartite Graphs

设G=(V,E)是一个无向简单图,a和b是两个非负整数,若函数f:E→[0,1]对所有的x∈V均满足a≤∑e∈xf(e)≤b,则称f为G的一个分数[a,b]-因子。此时,若还有a=b=k,则称f为G的一个分数k-因子,文章给出了偶图有分数k-因子的一个充分必要条件,并给出一个相关结论。

Let G = （ V, E） be a graph, a and b be two nonnegativeintegers, and f： E→0, 1] be a function. If a≤∑e∈xf（e）≤6 for all x ∈ V, fis called as a fractional [a, b]-factor of G. A fractional k-factorfis a fractional [ a, b]-factor with a = b = k. A necessary and sufficient condition for the fractional k-factors in the bipartite graphs is deduced. In addition, a concerning result is given ,