【摘要】 设图G=(X,Y,E)是二分图,g,f是定义在V(G)上的正整值函数,且对任意的x∈V(G)有g(x)<f(x),证明了:如果图G是(mg,mf-1)-图,M是G的任一含有m条边的对集,则存在图G的一个(g,f)-因子F,使F包含M任意给定的一条边,并且不包含其他的m-1条边;二分图G是(2m-1)-边连通的(mf)-图,则图G有一个f-因子包含任意给定的一条边,并且不包含任意其他的m-1条边.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).It is proved that if a G is the (mg,mf-1)-graph and M is a mathing with m edges,then G has a(g,f)-factor containing an edge of M and excluding other edges of M.If G is the(2m-1)-edge connected bipartite(mf)-graph,then G has an f-factor containing any given edge and excluding any given m-1 edges.更多还原