13 citations · 33 across the 14 of their papers we have counts for
14 papers
Duality and tangles of set separations
Reinhard Diestel, Christian Elbracht, Joshua Erde +1
Applications of tangles of connectivity systems suggest a duality between these, in which for two sets and the elements of map to subsets of , and the…
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…
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…
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…
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…
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 $ {…
Ubiquity in graphs II: Ubiquity of graphs with nowhere-linear end structure
Nathan Bowler, Christian Elbracht, Joshua Erde +4
A graph is said to be -ubiquitous, where is the minor relation between graphs, if whenever is a graph with for all , the…
Ubiquity in graphs I: Topological ubiquity of trees
Nathan Bowler, Christian Elbracht, Joshua Erde +4
Let be a relation between graphs. We say a graph is \emph{-ubiquitous} if whenever is a graph with for all $n \in \mathb…