Line transversals to unit disks
type: Item
instance of: scholarly article
title: Line transversals to unit disks
zbMATH Open document ID: 1021.52007
author: Tomáš Kaiser
published in: Discrete \& Computational Geometry
publication date: 2002-12-01T00:00:00Z
review text: Remember that a line transversal to a family of compact convex sets of Euclidean space is a straight line which intersects every set of this family. The author proves that if \(\mathcal F\) is a finite family of disjoint unit disks in the plane such that every three of those disks have a line transversal, then there exists a line which intersects all but at most \(C=12\) sets of \(\mathcal F\). He also outlines how his method applied to a family of translates of any plane compact convex set gives an analogical result with \(C=47\). The paper recalls other such general estimates, the currently best of which gives \(C=22\).
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 52A35
zbMATH DE Number: 1837073
zbMATH Keywords: line transversal
zbMATH Keywords: disk
zbMATH Keywords: compact convex set
MaRDI profile type: Publication
full work available at URL: s00454-002-2821-5
OpenAlex ID: W1977447061
DOI: 10.1007/S00454-002-2821-5
description: scientific article; zbMATH DE number 1837073