Abstract
A digraph is hamiltonian if it has a cycle that visits every vertex. If a digraph \(D\) is nonhamiltonian and \(D-v\) is hamiltonian for every \(v\in V(D)\), then \(D\) is said to be hypohamiltonian. It is known that there exist hypohamiltonian digraphs of order \(n\) for every \(n\ge 6\). Several infinite families of hypohamiltonian oriented graphs have appeared in the literature, but there are infinitely many orders which are not covered by those constructions. In this paper we construct a hypohamiltonian oriented graph of order \(n\) for every \(n\ge 9\).
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Acknowledgments
The authors wish to thank the University of South Africa for sponsoring the Salt Rock Workshop of 16–28 March 2014, which resulted in this paper.
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This material is based upon work supported by the National Research Foundation of South Africa under Grant Numbers 77248, 81004 and 81075.
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van Aardt, S.A., Burger, A.P., Frick, M. et al. Hypohamiltonian Oriented Graphs of All Possible Orders. Graphs and Combinatorics 31, 1821–1831 (2015). https://doi.org/10.1007/s00373-015-1561-2
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DOI: https://doi.org/10.1007/s00373-015-1561-2