# 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} }

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

### On longest non-Hamiltonian cycles in digraphs with the conditions of Bang-Jensen, Gutin and Li

- MathematicsDiscret. Appl. Math.
- 2017

### A new sufficient condition for a Digraph to be Hamiltonian-A proof of Manoussakis Conjecture

- Mathematics
- 2019

Y. Manoussakis (J. Graph Theory 16, 1992, 51-59) proposed the following conjecture.
\noindent\textbf{Conjecture}. {\it Let $D$ be a 2-strongly connected digraph of order $n$ such that for all…

### A Note on Hamiltonian Bypasses in Digraphs with Large Degrees

- Mathematics
- 2020

Let D be a 2-strongly connected directed graph of order p ≥ 3. Suppose that d(x) ≥ p for every vertex x ∈ V (D) \ {x0}, where x0 is a vertex of D. In this paper, we show that if D is Hamiltonian or…

## References

SHOWING 1-10 OF 20 REFERENCES

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

- MathematicsNinth 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…

### On longest non-Hamiltonian cycles in digraphs with the conditions of Bang-Jensen, Gutin and Li

- MathematicsDiscret. Appl. Math.
- 2017

### On Hamiltonian Bypasses in one Class of Hamiltonian Digraphs

- Mathematics
- 2014

Let $D$ be a strongly connected directed graph of order $n\geq 4$ which satisfies the following condition (*): for every pair of non-adjacent vertices $x, y$ with a common in-neighbour $d(x)+d(y)\geq…

### Long Cycles in Digraphs

- Mathematics
- 1981

Introduction By Ghouila-Houri's theorem [10], every strong digraph of order n and with minimum degree at least n is Hamiltonian. Extensions of this theorem can be found in [11, 13, 16, 18].…

### A sufficient condition for the hamiltonian property of digraphs with large semi-degrees

- Mathematics
- 2011

Let $D$ be a digraph on $p\geq 5$ vertices with minimum degree at least $p-1$ and with minimum semi-degree at least $p/2-1$. For $D$ (unless some extremal cases) we present a detailed proof of the…

### 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

- MathematicsJ. Graph Theory
- 1984

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…