Disjoint edges in complete topological graphs

  • Authors:
  • Andrew Suk

  • Affiliations:
  • MIT, Cambridge, MA, USA

  • Venue:
  • Proceedings of the twenty-eighth annual symposium on Computational geometry
  • Year:
  • 2012

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Abstract

It is shown that every complete $n$-vertex simple topological graph has at least Ω(n1/3) pairwise disjoint edges, and these edges can be found in polynomial time. This proves a conjecture of Pach and Toth, which appears as problem 5 from chapter 9.5 in Research Problems in Discrete Geometry by Brass, Moser, and Pach.