3 papers
math.CO2026
On ubiquity problems in infinite digraphs
Matthias Hamann, Karl Heuer
We prove that the consistently oriented double ray is ubiquitous if and only if it is ubiquitous restricted to the class of one-ended digraphs. Additionally, we prove the same equi…
math.CO2026
Infinite grids in digraphs
Matthias Hamann, Karl Heuer
Halin proved that every graph with an end containing infinitely many pairwise disjoint rays admits a subdivision of the infinite quarter-grid as a subgraph where all rays from…
math.CO2025
An end degree for digraphs
Matthias Hamann, Karl Heuer
In this paper we define a degree for ends of infinite digraphs. The well-definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion…