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A short proof that every finite graph has a tree-decomposition displaying its tangles
(ElsevierEuropean Journal of Combinatorics, 2016-06-08)
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 minors project of Robertson and Seymour and ...
A Liouville hyperbolic souvlaki
(Institute of Mathematical StatisticsElectronic Journal of Probability, 2017-04-25)
We construct a transient bounded-degree graph no transient subgraph of which embeds in any surface of finite genus.
Moreover, we construct a transient, Liouville, bounded-degree, Gromov–hyperbolic graph with trivial ...
Topological cycle matroids of infinite graphs
(ElsevierEuropean Journal of Combinatorics, 2017-02-01)
We prove that the topological cycles of an arbitrary infinite graph together with its topological ends form a matroid. This matroid is, in general, neither finitary nor cofinitary.