Girth and euclidean distortion

N. Linial*, A. Magen, A. Naor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Let G be a k-regular graph, k ≥ 3, with girth g. We prove that every embedding f : G → l2 has distortion Ω(√g). Two proofs are given, one based on Markov type [B] and the other on quadratic programming. In the core of both proofs are some Poincaré-type inequalities on graph metrics.

Original languageAmerican English
Pages (from-to)380-394
Number of pages15
JournalGeometric and Functional Analysis
Issue number2
StatePublished - 2002

Bibliographical note

Funding Information:
N.L. was supported in part by grants from the Israel Science Foundation and the Binational Science Foundation Israel-USA. A.N. was supported in part by the Binational Science Foundation Israel-USA and the Clore Foundation. This work is part of a Ph.D. thesis being prepared under the supervision of Professor Joram Lindenstrauss.


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