On a Gallai-type problem for lattices
type: Item
instance of: scholarly article
title: On a Gallai-type problem for lattices
zbMATH Open document ID: 0824.52008
DOI: 10.1007/BF01874358
published in: Acta Mathematica Hungarica
publication date: 1995-05-15T00:00:00Z
review text: The author proves the following Helly-type theorem, which is the planar lattice version of the Gallai problem: If \({\mathcal F}\) is a finite family of convex sets in \(E^ 2\), such that any 3 of them have a lattice point in common, then there exist 2 lattice points, which pin down \({\mathcal F}\) (i.e. each set contains at least one of these lattice points). Neither the `3' nor the `1' can be replaced, i.e. the result is tight.
Mathematics Subject Classification ID: 52A35
Mathematics Subject Classification ID: 52C05
zbMATH DE Number: 755497
zbMATH Keywords: Helly-type theorem
zbMATH Keywords: lattice
zbMATH Keywords: Gallai problem
author: Tamás Hausel
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: Q5824053
cites work: Q3738164
full work available at URL: https://doi.org/10.1007/bf01874358
OpenAlex ID: W2010662003
description: scientific article; zbMATH DE number 755497