English

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}
}
R2 v1 2026-06-22T07:56:56.773Z