Finite transitive graph embeddings into a hyperbolic metric space must stretch or squeeze

Itai Benjamini, Oded Schramm

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
EditorsBo'az Klartag, Shahar Mendelson, Vitali D. Milman
PublisherSpringer Verlag
Chapter5
Pages123-126
Number of pages4
ISBN (Print)9783642298486
DOIs
StatePublished - 29 May 2012

Publication series

NameLecture Notes in Mathematics
Volume2050

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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