On the ubiquity of oriented double rays
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866909194353901568 |
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| author | Gut, Florian Krill, Thilo Reich, Florian |
| author_facet | Gut, Florian Krill, Thilo Reich, Florian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the ubiquity of oriented double rays Gut, Florian Krill, Thilo Reich, Florian Combinatorics 05C20, 05C63 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. |
| title | On the ubiquity of oriented double rays |
| topic | Combinatorics 05C20, 05C63 |
| url | https://arxiv.org/abs/2310.09857 |