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Model. Anal. Inform. Sist., 2009, Volume 16, Number 2, Pages 22–74 (Mi mais52)  

This article is cited in 2 scientific papers (total in 2 papers)

On Erdős–Szekeres problem for empty hexagons in the plane

V. A. Koshelev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this work we consider a classical problem of Combinatorial Geometry of P. Erdős and G. Szekeres. The problem was posed in the 1930's. We investigate the minimum number $h(n)$ such, that for each $h(n)$-point set $A$ in general position in the plane there exists an $n$-point subset $B$ such, that the convex hull $C$ of $B$ is a convex empty $n$-gon, that is $(A\setminus B)\cap C=\emptyset$. Only recently T. Gerken has shown that $h(6)<\infty$. He has established the inequality $h(6)\le 1717$. The main result of the paper is the following inequality $h(6)\le 463$.

Keywords: general position, convex polygons, Ramsey theory

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UDC: 519+513
Received: 22.03.2009

Citation: V. A. Koshelev, “On Erdős–Szekeres problem for empty hexagons in the plane”, Model. Anal. Inform. Sist., 16:2 (2009), 22–74

Citation in format AMSBIB
\Bibitem{Kos09}
\by V.~A.~Koshelev
\paper On Erd\H os--Szekeres problem for empty hexagons in the plane
\jour Model. Anal. Inform. Sist.
\yr 2009
\vol 16
\issue 2
\pages 22--74
\mathnet{http://mi.mathnet.ru/mais52}


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    This publication is cited in the following articles:
    1. Raigorodskii A.M., “Izbrannye zadachi kombinatornoi geometrii i teorii grafov”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 3:4 (2011), 127–139  elib
    2. V. A. Koshelev, “Interior Points in the Erdős–Szekeres Theorems”, Math. Notes, 91:4 (2012), 542–557  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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