具有与任意图2-正交(g,f)的-因子分解的子图

Subgraphs with(g,f)-Factorization 2-Orthogonal to Any Graph

设g和f分别是定义在图G的顶点集合V(G)上的两个整数值函数且对每个x∈V(G)有3≤g(x)≤f(x)。本文证明了:若G是一个(mg+k,mf-k)-图,其中1≤k<m,则G中存在一个子图R满足对G的任一2k条边的子图H,R有一个(g,f) 因子分解与H2 正交。

Let g and f be two-integer-valued functions defined on V(G) such that 3≤g(x)<f(x) for each x∈V(G). This paper proved that for any 2k-subgraph H of an (mg+k,mf-k) -graph G,1≤k<m, there exists a subgraph R with a (g,f)-factorization 2-orthogonal to H.