(g,f)-消去图的若干充分条件

Some Sufficient Conditions of (g,f)-Deleted Graphs

设 G是一个图 ,用 V(G)和 E(G)表示它的顶点集和边集 ,并设 g和 f是定义在 V(G)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 F使对任意的 x∈V(G)有 g(x) d F(x) f (x) .如果对图 G的任意给定的边存在 G的一个 (g,f) -因子不含边 e,则称图 G是一个 (g,f ) -消去图 .本文分别给出了一个图是 (g,f ) -消去图的若干充分条件 .

Let G be a graph with vertex set V(G) and edge set E(G), and let g and f be two integer-valued functions defined on V(G) such that g<f for every x∈V(G). A (g,f)-factor of G is a spanning subgraph F of G such that g(x)d F(x)f(x) for every x∈V(G). A graph G is called a (g,f)-deleted graph if for every edge there is a (g,f)-factor of G such that it does not contain e. In this paper, some sufficient conditions for a graph to be (g,f)-deleted are given.