9-13 June 2013
Koper, Slovenia
UTC timezone
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Balanced 6-holes in bichromatic point sets

Presented by Ms. Birgit VOGTENHUBER
Type: Oral presentation
Track: Discrete and Computational Geometry

Content

We consider an Erd\H{o}s type question on $k$-holes (empty $k$-gons) in bichromatic point sets. For a bichromatic point set $S=R\union B$, %in general position and integer $k\geq2$, a balanced $2k$-hole in $S$ is %a simple polygon spanned by $k$ points of $R$ and $k$ points of $B$. %which does not contain any points of $S$ in its interior. We show that if $|R|=|B|=n$, then the number of balanced 6-holes in $S$ is at least $\frac{1}{45}n^2 - \Theta(n)$.

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Location: Koper, Slovenia

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