TY - JOUR
T1 - A SAT attack on the Erdos-Szekeres conjecture
AU - Balko, Martin
AU - Valtr, Pavel
N1 - Funding Information:
The authors were supported by the grant GACˇR 14-14179S. The first author was partially supported by the Grant Agency of the Charles University, GAUK 690214, and by the grant SVV-2015-260223. 2 Email: balko@kam.mff.cuni.cz 3 Webpage: http://kam.mff.cuni.cz/~valtr/
Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
KW - Convex position
KW - Erdos-Szekeres conjecture
KW - Ramsey number
KW - SAT solver
UR - http://www.scopus.com/inward/record.url?scp=84947763546&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2015.06.060
DO - 10.1016/j.endm.2015.06.060
M3 - Article
AN - SCOPUS:84947763546
SN - 1571-0653
VL - 49
SP - 425
EP - 431
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -