Maximal nontraceable graphs with toughness less than one (Q1010724)
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scientific article; zbMATH DE number 5540923
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximal nontraceable graphs with toughness less than one |
scientific article; zbMATH DE number 5540923 |
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Maximal nontraceable graphs with toughness less than one (English)
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7 April 2009
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Summary: A graph \(G\) is maximal nontraceable (MNT) if \(G\) does not have a Hamiltonian path but, for every \(e\in E(\overline{G}) \), the graph \(G+e\) has a Hamiltonian path. A graph \(G\) is 1-tough if for every vertex cut \(S\) of \(G\) the number of components of \(G-S\) is at most \(|S|\). We investigate the structure of MNT graphs that are not 1-tough. Our results enable us to construct several interesting new classes of MNT graphs.
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maximal nontraceable graph
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MNT
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Hamiltonian path
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tough graphs
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