Finding sets of points without empty convex 6-gons
type: Item
instance of: scholarly article
title: Finding sets of points without empty convex 6-gons
zbMATH Open document ID: 1019.52010
author: Mark H. Overmars
published in: Discrete \& Computational Geometry
publication date: 2003-03-17T00:00:00Z
review text: The author investigates a problem posed by Erdős which asks whether every large enough set of points in general position in the plane contains six points that form a convex \(6\)-gon without any points from the set in its interior. The author presents a fast incremental algorithm with which he was able to find a set of \(29\) points in the plane in general position which does not contain empty \(6\)-gons. In addition, using results obtained by the algorithm, a number of observations and conjectures are formulated about the possible structure of sets of points without empty convex \(6\)-gons.
reviewed by: Ferenc Fodor
Mathematics Subject Classification ID: 52C10
zbMATH DE Number: 1883360
zbMATH Keywords: convex hull
zbMATH Keywords: empty convex \(6\)-gons
zbMATH Keywords: Erdős problems
zbMATH Keywords: incremental algorithm
MaRDI profile type: Publication
full work available at URL: s00454-002-2829-x
OpenAlex ID: W2134189835
Wikidata QID: Q54152676
DOI: 10.1007/S00454-002-2829-X
description: scientific article; zbMATH DE number 1883360