13 citations · 28 across the 11 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…
Trees of tangles in infinite separation systems
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
We present infinite analogues of our splinter lemma from [Trees of tangles in abstract separation systems, arXiv:1909.09030]. From these we derive several tree-of-tangles-type theo…
Profinite tree sets
Jay Lilian Kneip
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separa…
Ends as tangles
Jay Lilian Kneip
Every end of an infinite graph defines a tangle of infinite order in . These tangles indicate a highly cohesive substructure in the graph if and only if they are closed…
Trees of tangles in abstract separation systems
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known tree-of-tangles t…
Representations of infinite tree-sets
J. Pascal Gollin, Jay Lilian Kneip
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We…
Tangles are Decided by Weighted Vertex Sets
Christian Elbracht, Jay Lilian Kneip, Maximilian Teegen
We show that, given a -tangle in a graph , there always exists a weight function such that a separation of of order $ {…
Separations of sets
Nathan Bowler, Jay Lilian Kneip
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize th…
Profinite separation systems
Reinhard Diestel, Jay Lilian Kneip
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be ex…