图的(g,f)—因子分解

(g,f)—Factorizations of Graphs

设Ｇ是一个图，ｇ和ｆ是定义在图Ｇ的顶点集上的两个整数值函数，且ｇ≤ｆ．图Ｇ的一个（ｇ，ｆ）—因子是Ｇ的一个支撑子图Ｈ，使对任意ｘ∈Ｖ（Ｈ）有ｇ（ｘ）≤ｄＨ（ｘ）≤ｆ（ｘ）．若图Ｇ的边集能划分为若干个边不相交的（ｇ，ｆ）—因子，则称Ｇ是（ｇ，ｆ）—可因子化的．给出了一个图是（ｇ，ｆ）—可因子化的一个充分条件，改进了有关结果．

Let G be a graph and g,f be two integer valued functions defined on V(G) such that g(x)≤f(x) for every x∈V(G).A (g,f)-factor of a graph G is a spanning subgraph H of G such that g(x)≤dH(x)≤f(x) for every x∈V(H).A graph G is said to be (g,f)-factorable if E(G) can be partitioned into several edge disjoint (g,f)-factors.In this paper,one sufficient condition for a graph to be (g,f)-factorable is given,which improves some results.