关于图是(g,f,n) -临界图的充分条件(英文)

Sufficient Conditions for Graphs to be(g,f,n)-critical Graphs

设 G是一个图 .设 g和 f是两个定义在 V(G)上的整值函数使得对 V(G)所有的顶点 x有 g(x) f (x) .图 G被称为 (g,f ,n) -临界图 ,如果删去 G的任意 n个顶点后的子图都含有 G的 (g,f ) -因子 .本文给出了图是 (a,b,n) -临界图几个充分条件 .进一步指出这些条件是最佳的 .例如 ,如果对 V(G)所有的顶点 x和 y都有 g(x) <f(x) ,n +g(x) d G(x)和 g(x) /(d G(x) - n) f (y) /d G(y) ,则 G是 (g,f ,n)

Let G be a graph, and let g and f be two integer-valued functions defined on V(G) such that g(x)f(x) for all x∈V(G). A graph G is called a (g,f,n)-critical graph if after deleting any n vertices of G the remaining graph of G has a (g,f) -factor. In this paper, sufficient conditions for graphs to be (g,f,n)-c ritical graphs are given. For example, we prove that a graph is a (g,f,n)-c ritical graph if g(x)<f(x) and n+g(x)d G(x) for all x∈V(G) and g(x)/(d G(x)-n)f(y)/d G(y) for all adjacent vertices x and y of G.