A SAT attack on the Erdős-Szekeres conjecture

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10313924" target="_blank" >RIV/00216208:11320/15:10313924 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S1571065315001067" target="_blank" >http://www.sciencedirect.com/science/article/pii/S1571065315001067</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.endm.2015.06.060" target="_blank" >10.1016/j.endm.2015.06.060</a>

Result language
angličtina
Original language name
A SAT attack on the Erdős-Szekeres conjecture
Original language description
A classical conjecture of Erdős and Szekeres states that every set of 2^(k MINUS SIGN 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 2^(k MINUS SIGN 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 Erdős, Tuza, and Valtr to refine the Erdős-Szekeres conjecture in order to tackle it with SAT solvers.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA14-14179S" target="_blank" >GA14-14179S: Algorithmic, structural and complexity aspects of configurations in the plane</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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