3 citations · 3 across the 5 of their papers we have counts for
5 papers
Separation profiles of hyperbolic planar and apex-minor-free graphs
Joseph P. MacManus, Bobby Miraftab
We show that the separation profile of a hyperbolic planar graph and, more generally, a hyperbolic apex-minor-free graph, grows at most logarithmically, answering a question of Ben…
Vertex cuts and median decompositions
Joseph P. MacManus, Bobby Miraftab
Median decompositions were introduced by Stavropoulos in 2015 as a generalisation of tree decompositions. In this paper, we further develop and exposit this theory as a tool in str…
A note on quasi-transitive graphs quasi-isometric to planar (Cayley) graphs
Joseph MacManus
Given a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph , we remark that one can upgrade to be a planar Cayley graph, answer…
The metric Menger problem
Júlia Baligács, Joseph MacManus
We study a generalization of the well-known disjoint paths problem which we call the metric Menger problem, denoted MM(r,k), where one is given two subsets of a graph and must deci…
Accessibility, planar graphs, and quasi-isometries
Joseph Paul MacManus
We prove that a connected, locally finite, quasi-transitive graph which is quasi-isometric to a planar graph is necessarily accessible. This leads to a complete classification of t…