Finite Transitive Graph Embeddings into a Hyperbolic Metric Space Must Stretch or Squeeze

  • Itai BenjaminiEmail author
  • Oded Schramm
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)


The δ-hyperbolicity constant of a finite vertex transitive graph with more than two vertices is proportional to its diameter. This implies that any map from such a graph into a 1-Gromov hyperbolic metric space has to stretch or squeeze the metric.


finite Vertex-transitive Graphs Geodesic Triangle Gromov Hyperbolic Groups Quasi Proof Geodesic Segment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael

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