Solving a conjecture about tessellation graphs of ${\mathbb{R}}^2$

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.

References in corpus (2)

• Hyperbolic Geometry of Complex Networks
• The Large Scale Curvature of Networks