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arXiv · 2310.09857

On the ubiquity of oriented double rays

Florian Gut·Thilo Krill·Florian Reich
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Abstract

A digraph $H$ is called ubiquitous if every digraph that contains arbitrarily many vertex-disjoint copies of $H$ also contains infinitely many vertex-disjoint copies of $H$. We study oriented double rays, that is, digraphs $H$ whose underlying undirected graphs are double rays. Calling a vertex of an oriented double ray a turn if it has in-degree or out-degree 2, we prove that an oriented double ray with at least one turn is ubiquitous if and only if it has a (finite) odd number of turns. It remains an open problem to determine whether the consistently oriented double ray is ubiquitous.

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Florian Gut, Thilo Krill, Florian Reich. 2023-10-15. On the ubiquity of oriented double rays. https://arxiv.org/abs/2310.09857

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