4 papers · 1 filter
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…
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…
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…