论文标题
在没有禁止子图的情况下，存在$ 2 $ factors
Existence of $2$-Factors in Tough Graphs without Forbidden Subgraphs
论文作者
论文摘要
对于给定的图形$ r $，如果$ g $不包含$ r $作为诱导子图，则图$ g $是$ r $ free。众所周知，至少三个顶点的每2 $ tough图都有$ 2 $ - factor。在具有限制结构的图表中，显示出每$ 2K_2 $ - FREE $ 3/2 $ -TOUGH图表至少三个顶点具有$ 2 $ -FACTOR，而韧性约束$ 3/2 $是最好的。在观看$ 2K_2 $的情况下，在本文中，对于5、6或7个顶点的任何线性森林$ r $ $ r $ $ r $ r $的脱节，我们发现每一个尖锐的韧性$ t $，因此，至少三个Vertices上的每个$ t $ r $ r $ r $ r $ - free-free Graph totertion tote toth toter toter toter toth thive tote totertices toter toter toter toter的图形至少有2-属性。
For a given graph $R$, a graph $G$ is $R$-free if $G$ does not contain $R$ as an induced subgraph. It is known that every $2$-tough graph with at least three vertices has a $2$-factor. In graphs with restricted structures, it was shown that every $2K_2$-free $3/2$-tough graph with at least three vertices has a $2$-factor, and the toughness bound $3/2$ is best possible. In viewing $2K_2$, the disjoint union of two edges, as a linear forest, in this paper, for any linear forest $R$ on 5, 6, or 7 vertices, we find the sharp toughness bound $t$ such that every $t$-tough $R$-free graph on at least three vertices has a 2-factor.
