Recent trends in Euclidean Ramsey theory
type: Item
instance of: scholarly article
title: Recent trends in Euclidean Ramsey theory
zbMATH Open document ID: 0816.05060
DOI: 10.1016/0012-365X(94)00110-5
published in: Discrete Mathematics
publication date: 1995-02-13T00:00:00Z
review text: The paper surveys several new results in Euclidean Ramsey theory. A finite set \(X\) in some Euclidean space \(E^k\) is called Ramsey if for all \(r\) there exists some \(N= N(X, r)\) such that for every partition of \(E^N\) into \(r\) subsets, some of these subsets contain a congruent copy of \(X\). Basic results concerning the unsolved question on the characterization of Ramsey sets are discussed. Also the question on the restriction to spheres is addressed. Moreover, density theorems, partition variants, results on the chromatic number of \(E^n\) (two points are joined by an edge if their distance is 1) and partition theorems in fixed dimension together with difficult conjectures are presented.
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 722488
zbMATH Keywords: Euclidean Ramsey theory
zbMATH Keywords: Euclidean space
zbMATH Keywords: partition
zbMATH Keywords: congruent copy
zbMATH Keywords: Ramsey sets
zbMATH Keywords: spheres
zbMATH Keywords: density theorems
zbMATH Keywords: chromatic number
author: Ron Graham
reviewed by: Konrad Engel
MaRDI profile type: Publication
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full work available at URL: 0012-365x(94)00110-5
OpenAlex ID: W2155217117
description: scientific article; zbMATH DE number 722488