图的孤立韧度与分数因子的存在性

ISOLATED TOUGHNESS AND THE EXISTENCE OF FRACTIONAL FACTORS

设G是一个简单无向图,若G不是完全图,G的孤立韧度定义为I(G)=min{ }.否则,令I(G)=∞.本文引入一个与图的孤立韧度I(G)密切相关的新参数I’(G),若G不是完全图时,I’(G)=min{ }.否则,I‘(G)=∞;本文研究了参数I(G)和I’(G)的性质以及两者与图的分数k-因子的关系.给出了具有某些约束条件的图的分数因子存在的一些充分条件.并提出进一步的可研究的问题.

Let G be a graph, the isolated toughness of G is defined as I(G) = min if is not complete. Otherwise, set I(G)=o. A variation of isolated toughness is defined as, I'(G) = min if G is not complete. Otherwise, I'(G) = o; In this paper, the relationship between the isolated toughness, the variation of isolated toughness and fractional factors of graphs is discussed; Sufficient conditions for graphs to have fractonal 1-factors and 2-factors with some constraints are given. Some new problems are presented.