15 citations · 34 across the 12 of their papers we have counts for
16 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…
Hamilton-laceable bi-powers of locally finite bipartite graphs
Karl Heuer
In this paper we strengthen a result due to Li by showing that the third bi-power of a locally finite connected bipartite graph that admits a perfect matching is Hamilton-laceable,…
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…
Even Circuits in Oriented Matroids
Karl Heuer, Raphael Steiner, Sebastian Wiederrecht
In this paper we generalise the even directed cycle problem, which asks whether a given digraph contains a directed cycle of even length, to orientations of regular matroids. We de…
Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs II: paws
Karl Heuer, Deniz Sarikaya
In this paper we extend a result about a sufficient condition for Hamiltonicity for finite graphs by Broersma and Veldmann to locally finite graphs. In order to do this we use topo…
Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs I: nets and bulls
Karl Heuer, Deniz Sarikaya
In a series of papers, of which this is the first, we study sufficient conditions for Hamiltonicity in terms of forbidden induced subgraphs and extend such results to locally finit…
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…
A sufficient local degree condition for Hamiltonicity in locally finite claw-free graphs
Karl Heuer
Among the well-known sufficient degree conditions for the Hamiltonicity of a finite graph, the condition of Asratian and Khachatrian is the weakest and thus gives the strongest res…
A sufficient condition for Hamiltonicity in locally finite graphs
Karl Heuer
Using topological circles in the Freudenthal compactification of a graph as infinite cycles, we extend to locally finite graphs a result of Oberly and Sumner on the Hamiltonicity o…
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…
Ubiquity in graphs II: Ubiquity of graphs with nowhere-linear end structure
Nathan Bowler, Christian Elbracht, Joshua Erde +4
A graph is said to be -ubiquitous, where is the minor relation between graphs, if whenever is a graph with for all , the…
Ubiquity in graphs I: Topological ubiquity of trees
Nathan Bowler, Christian Elbracht, Joshua Erde +4
Let be a relation between graphs. We say a graph is \emph{-ubiquitous} if whenever is a graph with for all $n \in \mathb…
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…
Infinite end-devouring sets of rays with prescribed start vertices
J. Pascal Gollin, Karl Heuer
We prove that every end of a graph contains either uncountably many disjoint rays or a set of disjoint rays that meet all rays of the end and start at any prescribed feasible set o…
Hamiltonicity in locally finite graphs: two extensions and a counterexample
Karl Heuer
We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs. We also give an…
Excluding a full grid minor
Karl Heuer
In this paper we characterise the graphs containing a grid minor in a similar way as it has been done by Halin for graphs with an $\mathbb{N} \times…