2023/10/15 by Florian Gut, Gut, Florian, Thilo Krill +3
Computer Science · Mathematics · Engineering · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2310.09857
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.