On Crossing-Families in Planar Point Sets
Computational Geometry
2022-10-03 v2 Combinatorics
Abstract
A -crossing family in a point set in general position is a set of segments spanned by points of such that all segments mutually cross. In this short note we present two statements on crossing families which are based on sets of small cardinality: (1) Any set of at least 15 points contains a crossing family of size 4. (2) There are sets of points which do not contain a crossing family of size larger than . Both results improve the previously best known bounds.
Cite
@article{arxiv.2109.10705,
title = {On Crossing-Families in Planar Point Sets},
author = {Oswin Aichholzer and Jan Kynčl and Manfred Scheucher and Birgit Vogtenhuber and Pavel Valtr},
journal= {arXiv preprint arXiv:2109.10705},
year = {2022}
}