Traffic Congestion in Expanders and (p,δ)–Hyperbolic Spaces

Abstract

In this article we define the notion of (p, δ)–Gromov hyperbolic space where we relax the Gromov slimness condition to allow that not all, but a positive fraction of all triangles, are δ–slim. Furthermore, we study their traffic congestion under geodesic routing. We also construct a constant degree family of expanders with congestion Θ(n2) in contrast to random regular graphs that have congestion O(nlog3(n)).