摘要
设G是一个图,具有顶点集V(G)和边集E(G).设g和f是定义在V(G)上的整数值函数且对每个x∈V(G)有g(x)≤f(x).本文证明了如下的结果:若G是一个(mg+kr,mf-kr)-图,且对每个x∈V(G)有g(x)≥r-1,H和G的任意给定的有kr条边的子图,则G中含有一个子图R,使R有(g,f)-因子分解r-正交于H,其中m,k和r是正整数且k<m.
Let G be a graph with vertex set V(G) and edge set E(G),and let ag and f be two integer-valued functions defined on V(G) such that g(x)≤f for all x∈V(G). In this paper it is proved that for any subgraph H with kr edges of an (mg+kr,mf-kr)-graph G, where m ,k and r are positive integers with k〈 m and g(x)≥r-1 for all x∈V(G),there exists a subgraph R with a (g,f)-factorization r-orthogonal to H.
出处
《数学理论与应用》
2005年第3期10-14,共5页
Mathematical Theory and Applications