Geodesic
Maximal nontraceable graphs with toughness less than one
The electronic journal of combinatorics, Tome 15 (2008)
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A graph $G$ is maximal nontraceable (MNT) if $G$ does not have a hamiltonian path but, for every $e\in E\left( \overline{G}\right) $, 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.
DOI : 10.37236/742
Classification : 05C38, 05C45
Mots-clés : maximal nontraceable graph, MNT, Hamiltonian path;tough graphs 
@article{10_37236_742,
     author = {Frank Bullock and Marietjie Frick and Joy Singleton and Susan van Aardt and Kieka (C.M.) Mynhardt},
     title = {Maximal nontraceable graphs with toughness less than one},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/742},
     zbl = {1180.05056},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/742/}
}
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Frank Bullock; Marietjie Frick; Joy Singleton; Susan van Aardt; Kieka (C.M.) Mynhardt. Maximal nontraceable graphs with toughness less than one. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/742

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