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%2F17%3A10363800" target="_blank" >RIV/00216208:11320/17:10363800 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.ejc.2017.06.010" target="_blank" >http://dx.doi.org/10.1016/j.ejc.2017.06.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2017.06.010" target="_blank" >10.1016/j.ejc.2017.06.010</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, for every integer k >= 2, every set of 2^(k - 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-2)+1 vertices contains an ordered subhypergraph with k vertices and k MINUS SIGN 2 edges, which is a union of a red monotone path and a blue monotone path that are vertex disjoint except for their two common end-vertices. Applying a 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>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-14179S" target="_blank" >GA14-14179S: Algorithmic, structural and complexity aspects of configurations in the plane</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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