图的正交(g,f)-因子分解

Orthogonal ( g,f) —Factorizations in Graphs

设ｇ和ｆ分别是定义在图Ｇ的顶点集合Ｖ（Ｇ）上的整数值函数且对每一个ｘ∈Ｖ（Ｇ）有２≤ｇ（ｘ）≤ｆ（ｘ）．证明了若Ｇ是（ｍｇ＋ｍ－１，ｍｆ－ｍ＋１）—图，则对Ｇ中任意一个给定的有ｍ条边的子图Ｈ，Ｇ有一个（ｇ，ｆ）—因子分解与Ｈ正交．

Let g and f be two integer valued functions defined on V(G) such that 2≤ g(x)≤f(x) for every x∈V(G) . In this paper, it is proved that for any subgraph H with m edges of a (mg+m-1,mf-m+1) —graph G , there exists a ( g,f) —factorization of G orthogonal to H .