Abstract
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.
O. Schramm
Oded died on September 1, 2008, while solo climbing Guye Peak in Washington State
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
O. Angel, I. Benjamini, Phase transition for the metric distortion of percolation on the hypercube. Combinatorica 27, 645–658 (2007)
I. Benjamini, Expanders are not hyperbolic. Isarel J. Math. 108, 33–36 (1998)
E. Ghys, A. Haefliger, A. Verjovsky (eds.), Groups Theory from a Geometrical Viewpoint (World Scientific, Singapore, 1991)
M. Gromov, Hyperbolic Groups, Essays in Group Theory, ed. by S. Gersten. MSRI Publications, vol. 8 (Springer, Berlin, 1987), pp. 75–265
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Benjamini, I., Schramm, O. (2012). Finite Transitive Graph Embeddings into a Hyperbolic Metric Space Must Stretch or Squeeze. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-29849-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29848-6
Online ISBN: 978-3-642-29849-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)