# A Note on Hamiltonian Bypasses in Digraphs with Large Degrees

## DOI:

https://doi.org/10.51408/1963-0055## Keywords:

Digraph, cycle, Hamiltonian cycle, Hamiltonian bypass## Abstract

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 d(x0) > 2(p − 1)/5, then D contains a Hamiltonian path, in which the initial vertex dominates the terminal vertex.

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*Mathematical Problems of Computer Science*,

*54*, 7–17. https://doi.org/10.51408/1963-0055