12 citations · 34 across the 21 of their papers we have counts for
11 papers · 2 filters
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…
A tree-of-tangles theorem for infinite tangles
Ann-Kathrin Elm, Jan Kurkofka
Carmesin has extended Robertson and Seymour's tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all…
Approximating infinite graphs by normal trees
Jan Kurkofka, Ruben Melcher, Max Pitz
We show that every connected graph can be approximated by a normal tree, up to some arbitrarily small error phrased in terms of neighbourhoods around its ends. The existence of suc…