图中具有推广的正交(g,f)-因子分解的子图

Subgraphs with Generalized Orthogonal (g,f)-Factorizations in Graphs

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.