关于图的(g,f)-因子分解

On (g, f)-Factorizations of Graghs

设G是一个图，g和f是定义在图G的顶点集V（G）上的两个非负整数值函数且g＜f．图G的一个（g，f）-因子是G的一个支撑子图F，使对所有的x∈V（G）有g（x）≤dF（x）≤f（x）．若G本身是一个（g，f）-因子，则称G是一个（g，f）-图．若G的边能分解成一些边不交的（g，f）-因子，则称G是（g，f）-因子可分解的．本文给出图G是(g，f)-因子可分解的一个充分条件．

Let G be a graph and g, f be two nonnegative-valued functions defined on the vertices set V(G) of G and g< f, A(g, f)-factor of a graph G is a spaning subgraph F of G such that g(x)<dF(x)<f(x) for all x(V(G). If G itselfis a (g, f)-factor, then it is said that G is a (g, f)-graph. If the edges of Gcan be decomposed into some edge disjoint (g, f)-factors, then it is called thatG is (g, f)-factorable. In this paper, one sufficient condition for a graph to be(g, f)-factorable is given.