Quasi-isometries between graphs with variable edge lengths
Combinatorics
2025-03-11 v1 Metric Geometry
Abstract
This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allowing for a bounded amount of additive and multiplicative distortion. Recently, Nguyen, Scott, and Seymour conjectured that, by appropriately adjusting the edge lengths of the target graph along with modifying the additive distortion constant, the multiplicative distortion factor could be eliminated. We disprove this conjecture.
Keywords
Cite
@article{arxiv.2503.07448,
title = {Quasi-isometries between graphs with variable edge lengths},
author = {James Davies and Meike Hatzel and Robert Hickingbotham},
journal= {arXiv preprint arXiv:2503.07448},
year = {2025}
}
Comments
7 pages, 1 figure