On Metric Ramsey-type Dichotomies

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The classical Ramsey theorem, states that every graph contains either a large clique or a large independent set. Here we investigate similar dichotomic phenomena in the context of finite metric spaces. Namely, we prove statements of the form "Every finite metric space contains a large subspace that is nearly quilateral or far from being equilateral". We consider two distinct interpretations for being "far from equilateral". Proximity among metric spaces is quantified through the metric distortion D. We provide tight asymptotic answers for these problems. In particular, we show that a phase transition occurs at D=2.
14 pages, 0 figures

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Combinatorics, 52C45; 05C55; 54E40; 05C12; 54E40

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http://salesiana.dossiersoluciones.com/handle/123456789/71606

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0406374
 http://arxiv.org/abs/math/0406374
 J. London Math. Society 71(2): 289-303, 2005
 doi:10.1112/S0024610704006155

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arXiv