Separation profiles of hyperbolic planar and apex-minor-free graphs
Combinatorics
2026-07-08 v1 Metric Geometry
Abstract
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 Benjamini, Schramm, and Tim\'ar in the affirmative.
Keywords
Cite
@article{arxiv.2607.07809,
title = {Separation profiles of hyperbolic planar and apex-minor-free graphs},
author = {Joseph P. MacManus and Bobby Miraftab},
journal= {arXiv preprint arXiv:2607.07809},
year = {2026}
}
Comments
16 pages, 2 figures; comments welcome!