关于图中子图的（n,k）—正交因子分解

设G是一个具有顶点集V(G)和边集E(G)的图. 设g和f是定义在V(G)上的两个整数值函数,使得g(x)f(x)对所有的点x∈V(G)都成立.如果G是一个(mg+n,mf-n)-图,1n<m2k,且g(x)2k-1对所有的点x∈V(G)都成立,则对任意给定具有|E(H)|=nk边的G的子图H,存在G的一个子图G′使G′有一个(g,f)-因子分解(n,k)-正交H.

On (n,k)-Orthogonal Factorizations in Subgraphs of Graphs

Let G be a graph with vertex set V(G) and edge set E(G), and let g and f be two integer-valued functions defined on V(G) such that g(x)f(x) for all x∈V(G). It is proved that if G is an (mg+n,mf-n)-graph, 1n＜m2k, and g(x)2k-1 for all x∈V(G), then there exists a subgraph G′ of G such that G′ has a (g,f)-factorization (n,k)-orthogonal to any given subgraph H of G with |E(H)|=nk.