12 citations · 34 across the 21 of their papers we have counts for
30 papers
An approximate cactus-decomposition for vertex-connectivity
Romain Bourneuf, Johannes Carmesin, Jan Kurkofka +1
The classical cactus theorem of Dinitz, Karzanov and Lomonosov from 1976 states that the minimum edge-cuts of a connected graph are displayed by a cactus. For vertex-separations, T…
A characterisation of all vertex-transitive finite graphs of connectivity < 5
Jan Kurkofka, Tim Planken
We characterise all vertex-transitive finite connected graphs as essentially 5-connected or on a short list of explicit graph-classes. Our proof heavily uses Tutte-type canonical d…
A Tutte-type canonical decomposition of 3- and 4-connected graphs
Jan Kurkofka, Tim Planken
We provide a unique decomposition of every 4-connected graph into parts that are either quasi-5-connected, cycles of triangle-torsos and 3-connected torsos on vertices, ge…
Canonical graph decompositions via local separations
Raphael W. Jacobs, Paul Knappe, Jan Kurkofka
Every finite graph can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like…
Towards a Stallings-type theorem for finite groups
Johannes Carmesin, George Kontogeorgiou, Jan Kurkofka +1
A recent development in graph-minor theory is to study local separators, vertex-sets that separate graphs locally but not necessarily globally. The local separators of a graph roug…
On the edge-chromatic number of 2-complexes
Jan Kurkofka, Emily Nevinson
We propose an open question that seeks to generalise the Four Colour Theorem from two to three dimensions. As an appetiser, we show that 12 instead of four colours are both suffici…
Characterising 4-tangles through a connectivity property
Johannes Carmesin, Jan Kurkofka
Every large -connected graph-minor induces a -tangle in its ambient graph. The converse holds for , but fails for . This raises the question whether `-conn…
Canonical Decompositions of 3-Connected Graphs
Johannes Carmesin, Jan Kurkofka
We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or…
The immersion-minimal infinitely edge-connected graph
Paul Knappe, Jan Kurkofka
We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an…
Canonical graph decompositions via coverings
Reinhard Diestel, Raphael W. Jacobs, Paul Knappe +1
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degre…
Entanglements
Johannes Carmesin, Jan Kurkofka
Robertson and Seymour constructed for every graph a tree-decomposition that efficiently distinguishes all the tangles in . While all previous constructions of these decompos…
A representation theorem for end spaces of infinite graphs
Jan Kurkofka, Max Pitz
End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is t…
The Lovász-Cherkassky theorem for locally finite graphs with ends
Raphael W. Jacobs, Attila Joó, Paul Knappe +2
Lovász and Cherkassky discovered independently that, if is a finite graph and such that the degree is even for every vertex , t…
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…
Countably determined ends and graphs
Jan Kurkofka, Ruben Melcher
The directions of an infinite graph are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets a c…
Edge-connectivity and tree-structure in finite and infinite graphs
Christian Elbracht, Jan Kurkofka, Maximilian Teegen
We show that every graph admits a canonical tree-like decomposition into its -edge-connected pieces for all simultaneously.
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…
The Farey graph is uniquely determined by its connectivity
Jan Kurkofka
We show that, up to minor-equivalence, the Farey graph is the unique minor-minimal graph that is infinitely edge-connected but such that every two vertices can be finitely separate…
End-faithful spanning trees in graphs without normal spanning trees
Carl Bürger, Jan Kurkofka
Schmidt characterised the class of rayless graphs by an ordinal rank function, which makes it possible to prove statements about rayless graphs by transfinite induction. Halin aske…
Every infinitely edge-connected graph contains the Farey graph or as a minor
Jan Kurkofka
We show that every infinitely edge-connected graph contains the Farey graph or as a minor. These two graphs are unique with this property up to minor-equival…
Duality theorems for stars and combs I: Arbitrary stars and combs
Carl Bürger, Jan Kurkofka
Extending the well-known star-comb lemma for infinite graphs, we characterise the graphs that do not contain an infinite comb or an infinite star, respectively, attached to a given…
Duality theorems for stars and combs II: Dominating stars and dominated combs
Carl Bürger, Jan Kurkofka
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the second paper of the seri…
Duality theorems for stars and combs III: Undominated combs
Carl Bürger, Jan Kurkofka
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. Here, in the third paper of the serie…
Duality theorems for stars and combs IV: Undominating stars
Carl Bürger, Jan Kurkofka
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we d…