Long Alternating Paths in Bicolored Point Sets

  • Jan Kynčl
  • János Pach
  • Géza Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)


Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length \(n+c\sqrt{n\over \log n}\). We disprove a conjecture of Erdős by constructing an example without any such path of length greater than \({4\over 3}n+c'\sqrt{n}\).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jan Kynčl
    • 1
  • János Pach
    • 2
  • Géza Tóth
    • 3
  1. 1.Department of Applied Mathematics and, Institute for Theoretical Computer ScienceCharles UniversityPragueCzech Republic
  2. 2.City College, CUNY and Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  3. 3.Rényi Institute, Hungarian Academy of SciencesBudapestHungary

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