Girth and Euclidean distortion

Nathan Linial*, Avner Magen, Assaf Naor

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


In this paper we partially prove a conjecture that was raised by Linial, London and Rabinovich in [11]. Let G be a k-regular graph, k ≥ 3, with girth g. We show that every embedding f : G → ℓ2 has distortion Ω(√g). The original conjecture which remains open is that the Euclidean distortion is bounded below by Ω(g). Two proofs are given, one based on semi-definite programming, and the other on Markov Type, a concept that considers random walks on metrics.

Original languageAmerican English
Pages (from-to)705-711
Number of pages7
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - 2002
EventProceedings of the 34th Annual ACM Symposium on Theory of Computing - Montreal, Que., Canada
Duration: 19 May 200221 May 2002

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