1 citations · 1 across the 4 of their papers we have counts for
14 papers
Agile Sets in Graphs
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
A set of vertices in a graph is agile if, however we partition the set into two parts, we can always find two vertex-disjoint connected subgraphs where one covers the first and the…
The Unravelling Problem
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
We identify and study a simple combinatorial problem that is derived from submodularity issues encountered in the theory of tangles of graphs and abstract separation systems.
The Structure of Submodular Separation Systems
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity con…
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…