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arXiv · 1706.00233

A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs

Samvel Kh. Darbinyan·Iskandar A. Karapetyan
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Abstract

Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 10$ other than a directed cycle. Let $x,y$ be distinct vertices in $D$. $\{x,y\}$ dominates a vertex $z$ if $x\rightarrow z$ and $y\rightarrow z$; in this case, we call the pair $\{x,y\}$ dominating. In this paper we prove: If $ max\{d(x), d(y)\}\geq 2a-2$ for every dominating pair of vertices $\{x,y\}$, then $D$ contains cycles of all lengths $2,4, \ldots , 2a-2$ or $D$ is isomorphic to a certain digraph of order ten which we specify.

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Samvel Kh. Darbinyan, Iskandar A. Karapetyan. 2017-06-01. A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs. https://arxiv.org/abs/1706.00233

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