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

@article{Darbinyan2014OnHB,
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={2014},
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…
3 Citations

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## References

SHOWING 1-10 OF 20 REFERENCES

### A note on long non-hamiltonian cycles in one class of Digraphs

• Mathematics
Ninth International Conference on Computer Science and Information Technologies Revised Selected Papers
• 2013
Let D be a strong digraph on n ≥ 4 vertices. In [3, Discrete Applied Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (*) d(x) + d(y) ≥ 2n-1 and

• Mathematics
• 2014

### Digraphs - theory, algorithms and applications

• Mathematics
• 2002
Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

### On the existence of a specified cycle in digraphs with constraints on degrees

We prove that Woodall's and Ghouila-Houri's conditions on degrees which ensure that a digraph is Hamiltonian, also ensure that it contains the analog of a directed Hamiltonian cycle but with one edge