# On Toughness and Hamiltonicity of 2K2‐Free Graphs

```@article{Broersma2014OnTA,
title={On Toughness and Hamiltonicity of 2K2‐Free Graphs},
author={Hajo Broersma and Viresh Patel and Artem V. Pyatkin},
journal={Journal of Graph Theory},
year={2014},
volume={75}
}```
• Published 1 March 2014
• Mathematics
• Journal of Graph Theory
The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields |A|/t components. Determining toughness is an NP‐hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class…
27 Citations
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