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New families of hypohamiltonian graphs

par Doyen, Jean ;Van Diest, Viviane
Référence Discrete mathematics, 13, 3, page (225-236)
Publication Publié, 1975

Article révisé par les pairs

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Résumé :

We construct three new infinite families of hypohamiltonian graphs having respectively 3k+1 vertices (k≥3), 3k vertices (k≥5) and 5k vertices (k≥4); in particular, we exhibit a hypohamiltonian graph of order 19 and a cubic hypohamiltonian graph of order 20, the existence of which was still in doubt. Using these families, we get a lower bound for the number of non-isomorphic hypohamiltonian graphs of order 3k and 5k. We also give an example of an infinite graph G having no two-way infinite hamiltonian path, but in which every vertex-deleted subgraph G - x has such a path. © 1975.