摘要
改进了关于ｒ－因子的结果，给出了一个图是ｒ－消去图的充分条件．并且用例子说明此结果是最好的可能．结果如下：定理Ⅰ设ｒ≥１是奇数，Ｇ是一简单图，且Ｖ（Ｇ）为偶数，如果ｋ（Ｇ）＞（ｒ＋１）２／２，且（ｒ＋１）２α（Ｇ）＜４ｒｘ（Ｇ），那么Ｇ为ｒ－消去图．定理Ⅱ设ｒ≥２为偶数，Ｇ是一简单图，如果ｋ（Ｇ）＞ｒ（＋２）／２，且（ｒ＋２）ａ（Ｇ）＜４ｋ（Ｇ），则Ｇ为ｒ－消去图．
Improves the results which are about r-factors, gives the sufficient condition,which is that a graph is r -deleted. Furthermore, through the examples, illustrates the possibility that the results are the best. The results are as follows: Theorems I Let r≥1 be an odd integer and G be a simple graph such that V(G) is even. If k(G) > (r+1)2/2 and (r + 1)2α(G) <, 4rk(G), then G is an r -deleted graph. Theorems Ⅱ Let r≥2 be an even integer and G be a simple graph. If k(G) > r(r + 2)/2 and (r + 2)α(G) <4k(G), then G is an r -deleted graph.
