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arXiv · 1801.05166

On Hamiltonian and Hamilton-connected digraphs

S. Kh. Darbinyan
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Abstract

C. Thomassen in \cite{[11]} suggested (see also \cite{[2]}, J. C.Bermond, C. Thomassen, Cycles in Digraphs - A survey, J. Graph Theory 5 (1981) 1-43, Conjectures 1.6.7 and 1.6.8) the following conjectures : 1. Every 3-strongly connected digraph of order $n$ and with minimum degree at least $n+1$ is strongly Hamiltonian-connected. 2. Let $D$ be a 4-strongly connected digraph of order $n$ such that the sum of the degrees of any pair of non-adjacent vertices is at least $2n+1$. Then $D$ is strongly Hamiltonian-connected. We disprove Conjecture 1 and prove two results which provide some support for Conjecture 2. The main goal of this article is to present the detailed proofs of these results (in English).

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S. Kh. Darbinyan. 2018-01-16. On Hamiltonian and Hamilton-connected digraphs. https://arxiv.org/abs/1801.05166

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