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

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

Carballosa, Walter. (2015). Solving a conjecture about tessellation graphs of $\mathbb R^2$ .

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.