43 citations · 147 across the 33 of their papers we have counts for
4 papers · 1 filter
The colouring number of infinite graphs
Nathan Bowler, Johannes Carmesin, Péter Komjáth +1
We show that, given an infinite cardinal , a graph has colouring number at most if and only if it contains neither of two types of subgraph. We also show that every graph wi…
A short proof that every finite graph has a tree-decomposition displaying its tangles
Johannes Carmesin
We give a short proof that every finite graph (or matroid) has a tree-decomposition that displays all maximal tangles. This theorem for graphs is a central result of the graph mino…
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…
Every planar graph with the Liouville property is amenable
Johannes Carmesin, Agelos Georgakopoulos
We introduce a strengthening of the notion of transience for planar maps in order to relax the standard condition of bounded degree appearing in various results, in particular, the…