43 citations · 147 across the 33 of their papers we have counts for
6 papers · 1 filter
Topological cycle matroids of infinite graphs
Johannes Carmesin
We prove that the topological cycles of an arbitrary infinite graph induce a matroid. This matroid in general is neither finitary nor cofinitary.
Infinite trees of matroids
Nathan Bowler, Johannes Carmesin
We generalise the construction of infinite matroids from trees of matroids to allow the matroids at the nodes, as well as the field over which they are represented, to be infinite.
All graphs have tree-decompositions displaying their topological ends
Johannes Carmesin
We show that every connected graph has a spanning tree that displays all its topological ends. This proves a 1964 conjecture of Halin in corrected form, and settles a problem of Di…
On the intersection conjecture for infinite trees of matroids
Nathan Bowler, Johannes Carmesin
Using a new technique, we prove a rich family of special cases of the matroid intersection conjecture. Roughly, we prove the conjecture for pairs of tame matroids which have a comm…
Even an infinite bureaucracy eventually makes a decision
Johannes Carmesin
We show that the fact that a political decision filtered through a finite tree of committees gives a determined answer generalises in some sense to infinite trees. This implies a n…
Topological infinite gammoids, and a new Menger-type theorem for infinite graphs
Johannes Carmesin
Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid. As our main to…