Near equipartitions of colored point sets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10360664" target="_blank" >RIV/00216208:11320/17:10360664 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.comgeo.2017.05.001" target="_blank" >http://dx.doi.org/10.1016/j.comgeo.2017.05.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.comgeo.2017.05.001" target="_blank" >10.1016/j.comgeo.2017.05.001</a>

Result language
angličtina
Original language name
Near equipartitions of colored point sets
Original language description
Suppose that nk points in general position in the plane are colored red and blue, with at least n points of each color. We show that then there exist n pairwise disjoint convex sets, each of them containing k of the points, and each of them containing points of both colors. We also show that if P is a set of n(d +1) points in general position in R^d colored by d colors with at least n points of each color, then there exist n pairwise disjoint d-dimensional simplices with vertices in P, each of them containing a point of every color. These results can be viewed as a step towards a common generalization of several previously known geometric partitioning results regarding colored point sets.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-14179S" target="_blank" >GA14-14179S: Algorithmic, structural and complexity aspects of configurations in the plane</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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