Abstract
A digraphD is called randomlyn-cyclic if for each vertexv ofD, every (directed) path with initial vertexv and having length at mostn − 1 can be extended to av − v (directed) cycle of lengthn. This notion was first introduced by Chartrand, Oellermann and Ruiz [3] and they determined all randomly 3, 4 and 5-cyclic diagraphs. In this paper, we will provide the characterization of randomlyn-cyclic digraphs forn ≥ 6.
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References
Chartrand, G., Kronk, H.V., Lick, D.R.: Randomly Hamiltonian digraphs. Fundam. Math.,45, 223–226 (1969)
Chartrand, G., Lesniak, L.: Graphs & Digraphs, 2nd edition. Monlerey: Wadsworth 1986
Chartrand, G., Oellermann, O. R., Ruiz, S.: Randomlyn-cyclic digraphs. Graphs and Combinatorics1, 29–40 (1985)
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Egawa, Y., Miyamoto, T. & Ruiz, S. On randomlyn-cyclic digraphs. Graphs and Combinatorics 3, 227–238 (1987). https://doi.org/10.1007/BF01788545
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DOI: https://doi.org/10.1007/BF01788545