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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 3 > No. 3


Avoiding Certain Graphs for a Variation of Toughness

PP: 243-248
Yaya Wang, Xiangguang He, Zhiqun Zhang, Wei Gao,
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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