On Sets of n Points in General Position That Determine Lines That Can Be Pierced by n Points

Chaya Keller, Rom Pinchasi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let P be a set of n points in general position in the plane. Let R be a set of n points disjoint from P such that for every x, y∈ P the line through x and y contains a point in R outside of the segment delimited by x and y. We show that P∪ R must be contained in cubic curve. This resolves a special case of a conjecture of Milićević. We use the same approach to solve a special case of a problem of Karasev related to a bipartite version of the above problem.

Original languageEnglish
Pages (from-to)905-915
Number of pages11
JournalDiscrete and Computational Geometry
Volume64
Issue number3
DOIs
StatePublished - 1 Oct 2020
Externally publishedYes

Keywords

  • Cubic curves
  • Elliptic curves
  • Line blocker
  • Lines
  • Points

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this