On metric ramsey-type dichotomies

Yair Bartal*, Nathan Linial, Manor Mendel, Assaf Naor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The classical Ramsey theorem states that every graph contains either a large clique or a large independent set. Here similar dichotomic phenomena are investigated in the context of finite metric spaces. Namely, statements are provided of the form 'every finite metric space contains a large subspace that is nearly equilateral or far from being equilateral'. Two distinct interpretations are considered for being 'far from equilateral'. Proximity among metric spaces is quantified through the metric distortion α. Tight asymptotic answers are provided for these problems. In particular, it is shown that a phase transition occurs at α = 2.

Original languageAmerican English
Pages (from-to)289-303
Number of pages15
JournalJournal of the London Mathematical Society
Issue number2
StatePublished - Apr 2005

Bibliographical note

Funding Information:
The first and second authors’ research was supported in part by grants from the Israeli National Science Foundation. The third author’s research was supported in part by the Landau Center.


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