图的参数与因子及分数因子的几个结果

Some results on parameters and factors and fractional factors of graphs

本文研究了图中两个重要的参数联结数和韧度,以及两个参数与因子和分数因子之间关系,并证明了图有分数因子的一个充分条件;还探讨了子图的结构,得出了子图的任一分支的韧度与图本身的韧度的关系。

Toughness and binding number are two important parameters in graph theory. In this paper, we study the relationship between parameters and factors, fractional factors of graphs. We prove a sufficient condition for the existence of fractional factors in graphs; we also explore the structure of subgraphs and give the relationship of the toughness of any branch of the graphs and their own.