Almost disjoint triangles in 3-space
type: Item
instance of: scholarly article
title: Almost disjoint triangles in 3-space
zbMATH Open document ID: 1024.52007
author: Gyula Károlyi
author: József Solymosi
published in: Discrete \& Computational Geometry
publication date: 2003-03-17T00:00:00Z
review text: Two triangles are called almost disjoint if their intersection is either empty or consists of one common vertex. Let \(f(n)\) denote the maximum number of pairwise almost disjoint triangles that can be found on some vertex set of \(n\) points in 3-space. A first construction of \(m^2+{m\choose 2}\) points which constitute the vertex set of \(m{m\choose 2}\) almost disjoint triangles shows that \(f(n)= \Omega(n^{3/2})\). A second construction based on cyclic polytopes confirms that result and leads to an open question: Is there, for \(n\) arbitrarily large, a closed polyhedral manifold in 3-space with \(n\) vertices whose genus is \(\Omega(n^{3/2})\)?
Mathematics Subject Classification ID: 52C10
Mathematics Subject Classification ID: 52B70
zbMATH DE Number: 1883343
zbMATH Keywords: almost disjoint triangles
zbMATH Keywords: cyclic polytopes
reviewed by: Jonathan Schaer
MaRDI profile type: Publication
full work available at URL: s00454-002-2888-z
OpenAlex ID: W2063474387
DOI: 10.1007/S00454-002-2888-Z
description: scientific article; zbMATH DE number 1883343