arXiv:2305.08512v1 [math.MG] 15 May 2023 Page 1 A COARSE-GEOMETRY
CHARACTERIZATION OF CACTI KOJI FUJIWARA AND PANOS PAPASOGLU Abstract. We give …

It was conjectured, independently by two sets of authors, that for all integers $ k, d\ge 1$
there exists $\ell> 0$, such that if $ S, T $ are subsets of vertices of a graph $ G $, then either …

We study geometric and topological properties of infinite graphs that are quasi-isometric to a
planar graph of bounded degree. We prove that every locally finite quasi-transitive graph …

Let $ A $ and $ B $ be sets of vertices in a graph $ G $. Menger's theorem states that for
every positive integer $ k $, either there exists a collection of $ k $ vertex-disjoint paths …

We disprove the conjecture of Georgakopoulos and Papasoglu that a length space (or
graph) with no $ K $-fat $ H $ minor is quasi-isometric to a graph with no $ H $ minor. Our …

We define coarse skeletons of graphs in terms of two constants. We introduce the notion of
coarse bottlenecking in graphs and show how it can guarantee that a skeleton resembles …

We give an approximate Menger-type theorem for the case when a graph contains two paths
and such that is an induced subgraph of. More generally, we prove that there exists a …

When does a graph admit a tree-decomposition in which every bag has small diameter? For
finite graphs, this is a property of interest in algorithmic graph theory, where it is called …

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 …

Given an arbitrary class $\mathcal {H} $ of graphs, we investigate which graphs admit a
decomposition modelled on a graph in $\mathcal {H} $ into parts of small radius. The …