二分图上有限制条件的(g,f)-因子分解(英文)

(g,f)-Factorization with constraints in bipartite graphs

设G=(X,Y,E)是二分图,g,f是定义在V(G)上的正整数值函数,且对任意的x∈V(G)有g(x)<f(x).令G是(mg,mf-1)-图,证明了:①若,g(x)≥1,H是G的任一含有m条边的子图.则G有一个(g,f)-因子分解与H-正交.②若g(x)≥2,H是G的任一含有2m条边的子图,则G有一个(g,f)-因子分解与H2-正交.

Let G = （ X, Y, E） be a bipartite graph and let g and f be two positive integer functions defined on V（G） with g（x） 〈f（x） for each x∈V（G）. Let G is （mg, mf-1）-graph. It is proved that ①if g（x）≥1, H is a subgraph of G with m edges, then G has a （g ,f）-factorization orthogonal to H;②if g（x）≥2, H is a subgraph of G with 2m edges, then G has a （g ,f）-faetorization 2-orthogonal to H.