4 papers
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…
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…
Periodic colorings and orientations in infinite graphs
Tara Abrishami, Louis Esperet, Ugo Giocanti +3
We study the existence of periodic colorings and orientations in locally finite graphs. A coloring or orientation of a graph is periodic if the resulting colored or oriented gr…
Quasi-transitive -minor free graphs
Matthias Hamann
We prove that every locally finite quasi-transitive graph that does not contain as a minor is quasi-isometric to some planar quasi-transitive locally finite graph. This…