【摘要】 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.更多还原

【Abstract】 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)-factorization 2-orthogonal to H.更多还原