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Gromov hyperbolicity and convex tessellation graph

Abstract

In [7] the following conjecture is stated: 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.

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Correspondence to W. Carballosa.

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Carballosa, W. Gromov hyperbolicity and convex tessellation graph. Acta Math. Hungar. 151, 24–34 (2017). https://doi.org/10.1007/s10474-016-0677-z

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Key words and phrases

  • hyperbolic graph
  • tessellation graph
  • geodesics
  • periodic graph

Mathematics Subject Classification

  • 05C10
  • 05C63
  • 05C99