A Ramsey property of order types
type: Item
instance of: scholarly article
title: A Ramsey property of order types
zbMATH Open document ID: 0902.52006
author: J. Nešetřil
author: Pavel Valtr
published in: Journal of Combinatorial Theory. Series A
publication date: 1998-12-03T00:00:00Z
review text: The main result of this paper is that for any finite set \(A\) of points in the plane, any fixed number \(k\) of colors, and any distance bound \(\varepsilon > 0\) there is a finite set \(B\) in the plane such that in any \(k\)-coloring of \(B\) there is a monochromatic subset \(C\) of \(B\) that is induced by its convex hull in \(B\) and that is an affine image of an \(\varepsilon\)-approximation of \(A\) in the Hausdorff sense. This implies a number of Ramsey-type theorems on the existence of subsets of a given order type, as well as on the distances forced by any realization of a given order type.
Mathematics Subject Classification ID: 52C10
Mathematics Subject Classification ID: 05D10
zbMATH DE Number: 1123549
zbMATH Keywords: order type
zbMATH Keywords: Ramsey property
zbMATH Keywords: combinatorial geometry
zbMATH Keywords: Hausdorff approximation
reviewed by: Peter Brass
MaRDI profile type: Publication
full work available at URL: jcta.1997.2820
OpenAlex ID: W2068227483
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DOI: 10.1006/JCTA.1997.2820
description: scientific article; zbMATH DE number 1123549