On the intersections of systems of curves
type: Item
instance of: scholarly article
title: On the intersections of systems of curves
zbMATH Open document ID: 0936.05083
author: Gelasio Salazar
published in: Journal of Combinatorial Theory. Series B
publication date: 1999-11-21T00:00:00Z
review text: Let \(i_m(n)\) be the minimum number of intersections in a family of \(n\) simple closed curves whose members have pairwise at least one and less than \(m\) common points, where no point of the plane is in more than two members of the family. It is proved that \(\lim_{n\to\infty}\left(i_m(n)\left/\right.\left(\begin{smallmatrix} n\\ 2\end{smallmatrix}\right)\right)= 2\). The author asks for a characaterization of simple closed curves \(C\) such that the maximum number of intersections between two curves similar to \(C\) is finite.
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 1347236
zbMATH Keywords: intersecting family
zbMATH Keywords: forbidden subgraph
zbMATH Keywords: convex set
zbMATH Keywords: simple closed curves
reviewed by: Konrad Engel
MaRDI profile type: Publication
full work available at URL: jctb.1998.1858
OpenAlex ID: W1982916807
cites work: Q4871771
cites work: Intersections of curve systems and the crossing number of \(C_ 5\times C_ 5\)
DOI: 10.1006/JCTB.1998.1858
description: scientific article; zbMATH DE number 1347236