6 papers
Disjoint dijoins for classes of dicuts in finite and infinite digraphs
J. Pascal Gollin, Karl Heuer, Konstantinos Stavropoulos
A dicut in a directed graph is a cut for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digra…
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…
On the Infinite Lucchesi-Younger Conjecture I
J. Pascal Gollin, Karl Heuer
A dicut in a directed graph is a cut for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digra…
Characterising -connected sets in infinite graphs
J. Pascal Gollin, Karl Heuer
A -connected set in an infinite graph, where is an integer, is a set of vertices such that any two of its subsets of the same size can be connected by $\el…
An analogue of Edmonds' Branching Theorem for infinite digraphs
J. Pascal Gollin, Karl Heuer
We extend Edmonds' Branching Theorem to locally finite infinite digraphs. As examples of Oxley or Aharoni and Thomassen show, this cannot be done using ordinary arborescences, whos…
Canonical tree-decompositions of a graph that display its -blocks
Johannes Carmesin, Pascal Gollin
A -block in a graph is a maximal set of at least vertices no two of which can be separated in by removing less than vertices. It is separable if there exists a t…