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SIAMDM
2010

Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons

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Large Bichromatic Point Sets Admit Empty Monochromatic 4-Gons
We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES (k) such that any set S of at least fES (k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in Ê2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).
Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Fe
Added 30 Jan 2011
Updated 30 Jan 2011
Type Journal
Year 2010
Where SIAMDM
Authors Oswin Aichholzer, Thomas Hackl, Clemens Huemer, Ferran Hurtado, Birgit Vogtenhuber
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