7 citations · 19 across the 19 of their papers we have counts for
20 papers
The global structure of locally chordal graphs
Tara Abrishami, Paul Knappe
A graph is locally chordal if each of its small-radius balls is chordal. In an earlier work [AKK25], the authors and Kobler proved that locally chordal graphs can be characterized…
Locally interval graphs are circular-arc graphs
Tara Abrishami, Sandra Albrechtsen, Nathan Bowler +2
Circular-arc graphs are graphs that can be represented as intersection graphs of subpaths of a cycle. Interval graphs are graphs that can be represented as intersection graphs of s…
Canonical tree-decompositions of chordal graphs
Raphael W. Jacobs, Paul Knappe
We show that a locally finite, connected graph is -locally chordal (that is, its -balls are chordal) if and only if the unique canonical graph-decomposition $\mathcal{H…
Locally chordal graphs
Tara Abrishami, Paul Knappe, Jonas Kobler
In this paper we study locally chordal graphs, i.e. graphs where every small-radius ball is chordal. We prove four characterizations of locally chordal graphs. Two are counterparts…
Canonical graph decompositions via local separations
Raphael W. Jacobs, Paul Knappe, Jan Kurkofka
Every finite graph can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like…
On vertex sets inducing tangles
Sandra Albrechtsen, Hanno von Bergen, Raphael W. Jacobs +2
Diestel, Hundertmark and Lemanczyk asked whether every -tangle in a graph is induced by a set of vertices by majority vote. We reduce their question to graphs whose size is boun…
Periodic colorings and orientations in infinite graphs
Tara Abrishami, Louis Esperet, Ugo Giocanti +3
We study the existence of periodic colorings and orientations in locally finite graphs. A coloring or orientation of a graph is periodic if the resulting colored or oriented gr…
A characterisation of graphs quasi-isometric to -minor-free graphs
Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe +1
We prove that there is a function such that every graph with no -fat minor is -quasi-isometric to a graph with no minor. This solves the -case of a ge…
Linked tree-decompositions into finite parts
Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe +1
We prove that every graph which admits a tree-decomposition into finite parts has a rooted tree-decomposition into finite parts that is linked, tight and componental. As an applica…
Counterexamples regarding linked and lean tree-decompositions of infinite graphs
Sandra Albrechtsen, Raphael W. Jacobs, Paul Knappe +1
Kriz and Thomas showed that every (finite or infinite) graph of tree-width admits a lean tree-decomposition of width . We discuss a number of counterexamples…
A structural duality for path-decompositions into parts of small radius
Sandra Albrechtsen, Reinhard Diestel, Ann-Kathrin Elm +4
It is an easy observation that if a graph~ admits a path-decomposition whose parts have small radius, then contains no large subdivision of or as a (quasi-)g…
A Menger-type theorem for two induced paths
Sandra Albrechtsen, Tony Huynh, Raphael W. Jacobs +2
We give an approximate Menger-type theorem for when a graph contains two paths and such that is an induced subgraph of . More generally, we…
Efficiently distinguishing all tangles in locally finite graphs
Raphael W. Jacobs, Paul Knappe
While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show t…
A grid theorem for strong immersions of walls
Reinhard Diestel, Raphael W. Jacobs, Paul Knappe +1
We show that a graph contains a large wall as a strong immersion minor if and only if the graph does not admit a tree-cut decomposition of small 'width', which is measured in terms…
The immersion-minimal infinitely edge-connected graph
Paul Knappe, Jan Kurkofka
We show that there is a unique immersion-minimal infinitely edge-connected graph: every such graph contains the halved Farey graph, which is itself infinitely edge-connected, as an…
Canonical graph decompositions via coverings
Reinhard Diestel, Raphael W. Jacobs, Paul Knappe +1
We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degre…
The Lovász-Cherkassky theorem for locally finite graphs with ends
Raphael W. Jacobs, Attila Joó, Paul Knappe +2
Lovász and Cherkassky discovered independently that, if is a finite graph and such that the degree is even for every vertex , t…
Base partition for mixed families of finitary and cofinitary matroids
Joshua Erde, Pascal Gollin, Attila Joó +2
Let be a finite or infinite family consisting of matroids on a common ground set each of which may be finitary or cofinitary. We prove the…
A Cantor-Bernstein-type theorem for spanning trees in infinite graphs
Joshua Erde, Pascal Gollin, Atilla Joó +2
We show that if a graph admits a packing and a covering both consisting of many spanning trees, where is some infinite cardinal, then the graph also admits a decomposition…
Circuits through prescribed edges
Paul Knappe, Max Pitz
We prove that a connected graph contains a circuit---a closed walk that repeats no edges---through any prescribed edges if and only if it contains no odd cut of size at most $k…