Planar point sets determine many pairwise crossing segments

János Pach, Natan Rubin, Gábor Tardos

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We show that any set of n points in general position in the plane determines n1−o(1) pairwise crossing segments. The best previously known lower bound, Ω n, was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

Original languageEnglish
Title of host publicationSTOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
EditorsMoses Charikar, Edith Cohen
Number of pages9
ISBN (Electronic)9781450367059
StatePublished - 23 Jun 2019
Event51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States
Duration: 23 Jun 201926 Jun 2019

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing


Conference51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019
Country/TerritoryUnited States


  • Avoiding edges
  • Comparability graphs
  • Computational geometry
  • Crossing edges
  • Extremal combinatorics
  • Geometric graphs
  • Intersection graphs
  • Partial orders

All Science Journal Classification (ASJC) codes

  • Software

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