关于图的k-因子的一个新结果

A New Result of k-factor of Graph

推证了命题设G是一个图 ,k是一个自然数。图G的一个k -正则生成子图称为G的一个k-因子。首先给出了一个图G有k -因子的一个充分条件 ,即若G是简单图 ,v是偶数且δ(G) v/ 2 +(k - 2 ) (这里k是整数且k 3) ,则G有k -因子。从而推广了文 [1]的一个结果 ,并得到了一个相关的结果。

This paper demonstrates the proposition that suppose G is a graph, k is a natural number, a k- in G generates a k- factor. Firstly, a sufficient condition for a k- factor in G is given, that is, if G is a simple graph, v is even number and δ(G)≥v/2+(k-2) (here, k is an integral number and k≥3), therefore, G possesses k-factor. In this way, a result from paper is extended and a relevant result is obtained.