On the size of maximally non-hamiltonian digraphs

Nicolas Lichiardopol, Carol T. Zamfirescu

Abstract


A graph is called maximally non-hamiltonian if it is non-hamiltonian, yet for any two non-adjacent vertices there exists a hamiltonian path between them. In this paper, we naturally extend the concept to directed graphs and bound their size from below and above. Our results on the lower bound constitute our main contribution, while the upper bound can be obtained using a result of Lewin, but we give here a different proof. We describe digraphs attaining the upper bound, but whether our lower bound can be improved remains open.


Keywords


Maximally non-hamiltonian digraphs

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DOI: https://doi.org/10.26493/1855-3974.1291.ee9

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications