On crossing-families in planar point sets

Oswin Aichholzer*, Jan Kynčl, Manfred Scheucher, Birgit Vogtenhuber, Pavel Valtr

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A k-crossing family in a point set S in general position is a set of k segments spanned by points of S such that all k 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 n points which do not contain a crossing family of size larger than [Formula presented]. Both results improve the previously best known bounds.

Original languageEnglish
Article number101899
JournalComputational Geometry: Theory and Applications
Publication statusPublished - Dec 2022


  • Crossing family
  • Geometric thrackle
  • Order type
  • Point set

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

Fields of Expertise

  • Information, Communication & Computing


Dive into the research topics of 'On crossing-families in planar point sets'. Together they form a unique fingerprint.

Cite this