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Դարբինյան Ս., Կարապետյան Ի., Дарбинян С., Карапетян И.
Title:
On pre-Hamiltonian Cycles in Hamiltonian Digraphs
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Creator:
Samvel Kh. Darbinyan ; Iskandar A. Karapetyan
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Uncontrolled Keywords:
Digraphs ; Cycles ; Hamiltonian cycles ; Pre-Hamiltonian cycles ; Longest non-Hamiltonian cycles.
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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+(z)≥3n-2. If there is no arc from z to x, then d(x)+d(y)+d-(x)+d+(z)≥3n-2. Then D is Hamiltonian.