二分(mg,mf)-图中的(g,f)-因子

设G是一个二分图具有顶点集V（G）和边集E（G）。设g和f是定义在V（G）上的两个正整值函数使对任意的x∈V（G）有g(x)≤f(x)，G的一个（g,f）－因子H是G的一个生成子图满足g(x)≤dH(x)≤f(x）。若图G本身是一个（g,f）－因子，则称G是一个（g,f）－图。本文得到一个（mg,mf）－图具有特殊性质的（g,f）－因子的充分条件，从而推广了文献[6]中的一个结果。

(g, f) - Factors in Bipartite (mg ,mf ) - Graphs

Let G be bipartite a graph with vertex set V(G)and edge set E(G)let g and f be two positive ingeger-valued functions defined on V(G)such that g(x)≤ f(x).A(g,f)- factor H of G is a spanning subgraph of G satisfying g(x)≤ dH(x)≤ f(x).A graph G is a(g,f)- graph means that G itself is a(g.f)- factor.In this paper sufficient conditions for a bipartite(mg,m f)- graph to have a(g,f)- factor with special properties are given.Therefore the result in[5]is generalized.