关于图的正交[0,k_i]_1~m—因子分解

On Orthogonal m 1 Factorizations of Graphs

设ｋ１，…，ｋｍ是正整数，若对每个ｘ∈Ｖ（Ｇ）有ｄＧ（ｘ）≤ｋ１＋…＋ｋｍ－ｍ＋１，Ｈ是Ｇ的一个ｍ－｛ｍ１—星，…，ｍｎ—星｝—子图，则图Ｇ有一个［０，ｋｉ］ｍ１—因子分解与Ｈ正交。

Let G be a graph, k 1,…k m be positive integers. If d G(x)≤k 1+…+k m-m+1 for all x∈V(G), and H is a m-{m 1 star ,…,m n star } graph in G, then G has a m 1 factorizations orthogonal to H.