On Hamiltonian bypasses in digraphs with the condition of Y. Manoussakis

@article{Darbinyan2015OnHB,
  title={On Hamiltonian bypasses in digraphs with the condition of Y. Manoussakis},
  author={Samvel Kh. Darbinyan},
  journal={2015 Computer Science and Information Technologies (CSIT)},
  year={2015},
  pages={53-63}
}
  • S. Darbinyan
  • Published 30 April 2014
  • Mathematics
  • 2015 Computer Science and Information Technologies (CSIT)
Let D be a strongly connected directed graph of order n ≥ 4 which 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. In [15] (J. of Graph Theory, Vol.16, No. 5, 51-59, 1992) Y. Manoussakis proved that D is Hamiltonian. In [9] it was shown that D contains a pre-Hamiltonian cycle (i.e., a cycle of length n-1… 

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