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arXiv · 1208.2164

On the Meyniel condition for hamiltonicity in bipartite digraphs

Janusz Adamus·Lech Adamus
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Abstract

We prove a sharp Meyniel-type criterion for hamiltonicity of a balanced bipartite digraph: For k greater than or equal to 2, a bipartite digraph D with colour classes of cardinalities k is hamiltonian if the sum of degrees of vertices u and v is at least 3k+1 for every pair of vertices u, v such that D does not contain the arc uv nor vu. As a consequence, we obtain a sharp sufficient condition for hamiltonicity in terms of the minimal degree: a balanced bipartite digraph D on 2k vertices is hamiltonian if its minimal degree is at least (3k + 1)/2.

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Janusz Adamus, Lech Adamus. 2012-08-10. On the Meyniel condition for hamiltonicity in bipartite digraphs. https://arxiv.org/abs/1208.2164

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