On Ramsey sets in spheres
type: Item
instance of: scholarly article
title: On Ramsey sets in spheres
zbMATH Open document ID: 0820.05060
DOI: 10.1016/0097-3165(95)90078-0
author: Vojtěch Rödl
author: Jiří Matoušek
published in: Journal of Combinatorial Theory. Series A
publication date: 1995-04-04T00:00:00Z
review text: It is shown that if \(L\) is the vertex set of a simplex of circumradius 1 in \(m\)-dimensional Euclidean space, and if a natural number \(r\) and \(\varepsilon > 0\) are given, then there is a natural number \(N\) such that for every \(r\)-coloring of a sphere of radius \(1 + \varepsilon\) in \(N\)- dimensional space there is a monochromatic congruent copy of \(L\). With \(\varepsilon = 0\) this is not true for most configurations.
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 05B30
zbMATH DE Number: 740285
zbMATH Keywords: Ramsey sets
zbMATH Keywords: coloring
zbMATH Keywords: geometric Ramsey theory
zbMATH Keywords: simplex
zbMATH Keywords: Euclidean space
zbMATH Keywords: sphere
zbMATH Keywords: configurations
reviewed by: Péter Komjáth
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90078-0
OpenAlex ID: W2088168476
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description: scientific article; zbMATH DE number 740285