二分图的与星正交的(g,f)-因子分解

A (g,f)factorization orthogonal to a star of a bipartite graph

设ｇ和ｆ是定义在二分图Ｇ的顶点集Ｖ（Ｇ）上的两个整数值函数且对每个ｘ∈Ｖ（Ｇ）有ｇ（ｘ）≤ｆ（ｘ）．证明了若Ｈ是二分图Ｇ的任一ｍ－星，则Ｇ有一个（ｇ，ｆ）－因子分解与Ｈ正交的充要条件是Ｇ为一个（ｍｇ，ｍｆ）－图．

Let G be a bipartite graph and g,f be two integervalued functions defined on the vertices set V(G) of G and g≤f. It is proved that if H is a mstar, then G has a (g,f)factorization orthogonal to H if and only if G is a (mg,mf)graph.