Solving a conjecture about tessellation graphs of $\mathbb R^2$
Metric Geometry
2020-01-23 v1 Combinatorics
Abstract
In the paper Planarity and Hyperbolicity in Graphs, the authors present the following conjecture: every tessellation of the Euclidean plane with convex tiles induces a non-hyperbolic graph. It is natural to think that this statement holds since the Euclidean plane is non-hyperbolic. Furthermore, there are several results supporting this conjecture. However, this work shows that the conjecture is false.
Keywords
Cite
@article{arxiv.1501.02288,
title = {Solving a conjecture about tessellation graphs of $\mathbb R^2$},
author = {Walter Carballosa},
journal= {arXiv preprint arXiv:1501.02288},
year = {2020}
}