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- W3212560749 abstract "Let D be a strongly connected directed graph of order n ≥ 4. In [14] (J. of Graph Theory, Vol.16, No. 5, 51-59, 1992) Y. Manoussakis proved the following theorem: Suppose that D satisfies the following condition for every triple x, y, z of vertices such that x and y are nonadjacent: If there is no arc from x to z, then d(x)+d(y)+d +(x)+ d i(z) ≥ 3n–2. If there is no arc from z to x, then d(x)+d(y)+d i(x)+d +(z) ¸ 3ni2. Then D is Hamiltonian. In this paper we show that: If D satisfies the condition of Manoussakis' theorem, then D contains a pre-Hamiltonian cycle (i.e., a cycle of length n i 1) or n is even and D is isomorphic to the complete bipartite digraph with partite sets of cardinalities n=2 and n=2." @default.
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- W3212560749 date "2014-04-30" @default.
- W3212560749 modified "2023-09-23" @default.
- W3212560749 title "On pre-Hamiltonian Cycles in Hamiltonian Digraphs" @default.
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