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Ubiquity in graphs III: Ubiquity of locally finite graphs with extensive tree-decompositions
Nathan Bowler, Christian Elbracht, Joshua Erde +4
A graph is said to be ubiquitous, if every graph that contains arbitrarily many disjoint -minors automatically contains infinitely many disjoint -minors. The well-kno…
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.
Obtaining trees of tangles from tangle-tree duality
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strength…
A canonical tree-of-tangles theorem for structurally submodular separation systems
Christian Elbracht, Jay Lilian Kneip
We show that every structurally submodular separation system admits a canonical tree set which distinguishes its tangles.
Clustering with Tangles: Algorithmic Framework and Theoretical Guarantees
Solveig Klepper, Christian Elbracht, Diego Fioravanti +4
Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of ta…
A Note on Generic Tangle Algorithms
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
In this note we gather the theoretical outlines of three basic algorithms for tangles in abstract separation systems: a naive tree search for finding tangles; an algorithm which ou…