# 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} }

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…

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