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Avoiding Certain Graphs for a Variation of Toughness |
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PP: 243-248 |
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Author(s) |
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Yaya Wang,
Xiangguang He,
Zhiqun Zhang,
Wei Gao,
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Abstract |
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| For an undirected simple
graph $G$, a variation of toughness is defined as
$$\tau(G)=\min\{\frac{|S|}{\omega(G-S)-1}\Big{|}\omega(G-S)\ge2
\}$$
if $G$ is not complete, and $\tau(G)=\infty$ if $G$ is complete.
In this paper, we determine the connected graph families
$\mathcal{F}$ such that every large enough connected
$\mathcal{F}$-free graph is $\tau$-tough. |
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