20 papers · 1 filter
A strengthening of Halin's grid theorem
Jan Kurkofka, Ruben Melcher, Max Pitz
We show that for every infinite collection of disjoint equivalent rays in a graph there is a subdivision of the hexagonal half-grid in such that all its verti…
Ubiquity in graphs III: Ubiquity of locally finite graphs with extensive tree-decompositions
Nathan Bowler, Christian Elbracht, Joshua Erde +4
A graph is said to be ubiquitous, if every graph that contains arbitrarily many disjoint -minors automatically contains infinitely many disjoint -minors. The well-kno…
Orientations of infinite graphs
Marcel Koloschin, Max Pitz
Building on recent work by Thomassen, we show that Nash-Williams' orientation theorem, that every finite -edge-connected multigraph has a -arc-connected orientation, also ho…
Halin's end degree conjecture
Stefan Geschke, Jan Kurkofka, Ruben Melcher +1
An end of a graph is an equivalence class of rays, where two rays are equivalent if there are infinitely many vertex-disjoint paths between them in . The degree of an end is…
Quickly proving Diestel's normal spanning tree criterion
Max Pitz
We present two short proofs for Diestel's criterion that a connected graph has a normal spanning tree provided it contains no subdivision of a countable clique in which every edge…
A note on minor antichains of uncountable graphs
Max Pitz
A simplified construction is presented for Komjáth's result that for every uncountable cardinal , there are graphs of size none of them being a minor of another.