An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of
its automorphism group. In this paper we obtain a structure theorem for locally finite quasi …

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 …

We prove that every locally finite, quasi-transitive graph with a thick end whose cycle space
is generated by cycles of bounded length contains the full-grid as an asymptotic minor and …

We prove that every locally finite quasi-transitive graph that does not contain K∞ as a minor
is quasi-isometric to some planar quasi-transitive locally finite graph. This solves a problem …

A recent development in graph theory is to study local separators, vertex sets that need not
separate graphs globally but just locally. We use this idea to conjecture an extension of …

We show that if G is a finitely generated group hyperbolic relative to a finite collection of
subgroups P, then the natural action of G on the geodesic boundary of the associated …

Let $ G $ be a quasi-transitive, locally finite, connected graph rooted at a vertex $ o $, and let
$ c_n (o) $ be the number of self-avoiding walks of length $ n $ on $ G $ starting at $ o $. We …

In an early work from 1896, Maschke established the complete list of all finite planar Cayley
graphs. This result initiated a long line of research over the next century, aiming at …

We study the existence of periodic colorings and orientations in locally finite graphs. A
coloring or orientation of a graph $ G $ is periodic if the resulting colored or oriented graph is …

We study subsets $ E $ of finitely generated groups where the set of all words over a given
finite generating set that lie in $ E $ forms a context-free language. We call these sets …