More on an Erdős-Szekeres-type problem for interior points
type: Item
instance of: scholarly article
title: More on an Erdős-Szekeres-type problem for interior points
zbMATH Open document ID: 1187.52017
author: Xianglin Wei
author: Ren Ding
published in: Discrete \& Computational Geometry
publication date: 2009-12-14T00:00:00Z
review text: As a variant of the well-known Erdős--Szekeres problem, \textit{D. Avis, K. Hosono} and \textit{M. Urabe} [Discrete Math. 241, 33--40 (2001; Zbl 1087.52505)] investigated the following problem: for every integer \(k\geq 1\), determine the smallest integer \(g(k)\), such that every set \(A\) of points in general position in the plane, which has at least \(g(k)\) points in the interior of the convex hull of \(A\), has a subset \(B\), which has exactly \(k\) of its points in the interior of the convex hull of \(B\). They showed \(g(1)=1\), \(g(2)=4\) and \(g(3)\geq 8\). The existence of \(g(k)\) is still open. The paper under review shows \(g(3)=9\).
reviewed by: László A. Székely
Mathematics Subject Classification ID: 52C10
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 5646260
zbMATH Keywords: Erdős--Szekeres problem
zbMATH Keywords: empty convex polygon
zbMATH Keywords: general position
zbMATH Keywords: interior point
zbMATH Keywords: deficient point set
zbMATH Keywords: splitter
MaRDI profile type: Publication
full work available at URL: s00454-008-9090-x
OpenAlex ID: W2041321344
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DOI: 10.1007/S00454-008-9090-X
description: scientific article; zbMATH DE number 5646260