1 citations · 2 across the 3 of their papers we have counts for
6 papers · 1 filter
Connecting vertex sets to walls
Henning Bruhn, Felix Joos, Arthur Ulmer
Menger's theorem on ---paths and Gallai's theorem on -paths are among the most useful results in structural graph theory. Many variants and extensions are known. We add to…
Zero -paths and the Erdős-Pósa property
Arthur Ulmer
Let be an Abelian group. In this paper I characterize the -paths of weight that have the Erdős-Pósa property. Using this in an auxiliary graph, one can also easily c…
Erdős-Pósa from ball packing
Wouter Cames van Batenburg, Gwenaël Joret, Arthur Ulmer
A classic theorem of Erdős and Pósa (1965) states that every graph has either vertex-disjoint cycles or a set of vertices meeting all its cycles. While the standa…
Long --paths have the edge-Erd\H os-Pósa property
Matthias Heinlein, Arthur Ulmer
For a fixed integer a path is long if its length is at least . We prove that for all integers and there is a number such that for every graph $G…
Packing A-Paths of Length Zero Modulo Four
Henning Bruhn, Arthur Ulmer
We show that A-paths of length 0 modulo 4 have the Erdős-Pósa property. We also prove that A-paths of length 2 modulo 4 have the property but that A-paths of length 1 or of length…
Directed cycles have the edge-Erd\H os-Pósa property
Matthias Heinlein, Arthur Ulmer
In this short note we prove that for every there is a such that for every digraph there are either edge-disjoint directed cycles in …