两类有向图的正交因子分解

Orthogonal Factorization for Two Classes of Digraph

研究了两类有向图的正交因子分解问题,得到如下结论:1)设G是(mg+nk,mf-nk)-有向图,其中1≤n<m,H是G的任意一个有nk条边的有向子图,其中g≥k≥1.则G中存在子图R,R具有(g,f)-因子分解k-正交于H;2)设G是(0,mf-m+1)-有向图,则对G中任意给定的有向2m-星K1,2m,G有一个(0,f)-因子分解2-正交于K1,2m.

After studying orthogonal factorization for two classes of digraph,the results are： 1） Let G be a（mg＋nk,mf-nk）-digraph,where 1≤n〈m.H is a subdigraph of G with nk edges and g≥k≥1,then there is subdigraph R of G,and R has a（g,f）-factorization k-orthogonal to H;2） there exists（0,f）-factorization orthogonal to any 2m-star K1,2m in a（0,mf-m＋1）-digraph.