A SAT attack on the Erdos-Szekeres conjecture

Martin Balko, Pavel Valtr

Research output: Contribution to journalArticlepeer-review


A classical conjecture of Erdos and Szekeres states that every set of 2k-2+1 points in the plane in general position contains k points in convex position. In 2006, Peters and Szekeres introduced the following stronger conjecture: every red-blue coloring of the edges of the ordered complete 3-uniform hypergraph on 2k-2+1 vertices contains an ordered k-vertex hypergraph consisting of a red and a blue monotone path that are vertex disjoint except for the common end-vertices.Applying the state of art SAT solver, we refute the conjecture of Peters and Szekeres. We also apply techniques of Erdos, Tuza, and Valtr to refine the Erdos-Szekeres conjecture in order to tackle it with SAT solvers.

Original languageEnglish
Pages (from-to)425-431
Number of pages7
JournalElectronic Notes in Discrete Mathematics
StatePublished - 1 Nov 2015
Externally publishedYes


  • Convex position
  • Erdos-Szekeres conjecture
  • Ramsey number
  • SAT solver

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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