License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2016.5
URN: urn:nbn:de:0030-drops-58972
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5897/
Ackerman, Eyal ;
Keszegh, Balázs ;
Vizer, Máté
Coloring Points with Respect to Squares
Abstract
We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a constant m such that any finite set S of points in the plane can be 2-colored such that every axis-parallel square that contains at least m points from S contains points of both colors. Our proof is constructive, that is, it provides a polynomial-time algorithm for obtaining such a 2-coloring. By affine transformations this result immediately applies also when considering homothets of a fixed parallelogram.
BibTeX - Entry
@InProceedings{ackerman_et_al:LIPIcs:2016:5897,
author = {Eyal Ackerman and Bal{\'a}zs Keszegh and M{\'a}t{\'e} Vizer},
title = {{Coloring Points with Respect to Squares}},
booktitle = {32nd International Symposium on Computational Geometry (SoCG 2016)},
pages = {5:1--5:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-009-5},
ISSN = {1868-8969},
year = {2016},
volume = {51},
editor = {S{\'a}ndor Fekete and Anna Lubiw},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5897},
URN = {urn:nbn:de:0030-drops-58972},
doi = {10.4230/LIPIcs.SoCG.2016.5},
annote = {Keywords: Geometric hypergraph coloring, Polychromatic coloring, Homothets, Cover-decomposability}
}
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Keywords: |
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Geometric hypergraph coloring, Polychromatic coloring, Homothets, Cover-decomposability |
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Collection: |
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32nd International Symposium on Computational Geometry (SoCG 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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10.06.2016 |
