On k-gons and k-holes in point sets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317584" target="_blank" >RIV/00216208:11320/15:10317584 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.comgeo.2014.12.007" target="_blank" >http://dx.doi.org/10.1016/j.comgeo.2014.12.007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.comgeo.2014.12.007" target="_blank" >10.1016/j.comgeo.2014.12.007</a>

Result language
angličtina
Original language name
On k-gons and k-holes in point sets
Original language description
We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show bounds and structural results on maximizing and minimizing their numbers. Most noteworthy, for any k and sufficiently large n, we give a quadratic lower bound for the number of k-holes, and show that this number is maximized by sets in convex position.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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