Acta Mathematica Hungarica

, Volume 151, Issue 1, pp 24–34

Gromov hyperbolicity and convex tessellation graph

Article

DOI: 10.1007/s10474-016-0677-z

Cite this article as:
Carballosa, W. Acta Math. Hungar. (2017) 151: 24. doi:10.1007/s10474-016-0677-z
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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.

Mathematics Subject Classification

05C10 05C63 05C99 

Key words and phrases

hyperbolic graph tessellation graph geodesics periodic graph 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsFlorida International UniversityMiamiU.S.A.
  2. 2.Department of MathematicsMiami Dade CollegeMiamiU.S.A.