26 research outputs found
16th Scandinavian Symposium and Workshops on Algorithm Theory: SWAT 2018, June 18-20, 2018, Malmö University, Malmö, Sweden
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27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany
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Large bichromatic point sets admit empty monochromatic 4-gons
No full textWe 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).Postprint (published version
LIPIcs, Volume 261, ICALP 2023, Complete Volume
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