arXiv
Open Access
2023
On the ubiquity of oriented double rays
Florian Gut
Thilo Krill
Florian Reich
Abstrak
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.
Topik & Kata Kunci
Penulis (3)
F
Florian Gut
T
Thilo Krill
F
Florian Reich
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2023
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- en
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- arXiv
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- Open Access ✓