Large bichromatic point sets admit empty monochromatic 4-gons
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Tipus de documentText en actes de congrés
Data publicació2009
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Abstract
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 R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).
CitacióAichholzer, O. [et al.]. Large bichromatic point sets admit empty monochromatic 4-gons. A: European Workshop on Computational Geometry. "25th European Workshop on Computational Geometry". 2009, p. 133-136.
Versió de l'editorhttp://2009.eurocg.org/abstracts.pdf
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