Abstract.
For a strongly connected digraph D, the k-th power D k of D is the digraph with the same set of vertices, a vertex x being joined to a vertex y in D k if the directed distance from x to y in D is less than or equal to k. It follows from a result of Ghouila-Houri that for every digraph D on n vertices and for every k≥n/2, D k is hamiltonian. In the paper we characterize these digraphs D of odd order whose (⌈n/2 ⌉−1)-th power is hamiltonian.
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Revised: June 13, 1997
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Marczyk, A. On Hamiltonian Powers of Digraphs. Graphs Comb 16, 103–113 (2000). https://doi.org/10.1007/s003730050007
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DOI: https://doi.org/10.1007/s003730050007