3 papers
math.CO2026
A coarse Halin Grid Theorem with applications to quasi-transitive, locally finite graphs
Sandra Albrechtsen, Matthias Hamann
We prove a coarse version of Halin's Grid Theorem: Every one-ended, locally finite graph that contains the disjoint union of infinitely many rays as an asymptotic minor also contai…
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.CO2025
Asymptotic half-grid and full-grid minors
Sandra Albrechtsen, Matthias Hamann
We prove that every locally finite, quasi-transitive graph with a thick end whose cycle space is generated by cycles of bounded length contains the full-grid as an asymptotic minor…