图的韧度与分数k-因子的存在性

Toughness and the Existence Of Fractional k-Factors

设G是一个简单无向图,若G不是完全图,G的韧度的一个变形定义为τ(G)=m in{S/(ω(G-S)-1)∶S V(G),ω(G-S)2}.否则,令τ(G)=∞.本文研究了参数τ(G)与分数k-因子的关系,给出了具有某些约束条件的图的分数k-因子存在的一些充分条件,并提出进一步可研究的问题.

Let G be a graph, a variation of toughness is defined as r（G） = min {｜S｜/（w（G-S）-1）：S增包含V（G）,w（G-S）≥2） if G is not complete, and r（G） = co if G is complete. In this paper, the relationship between the variation of toughness and fractional k -factors of graphs is discussed. Some sufficient conditions for graphs to have fractional k-factors with some constraints are given. A new problem is presented.