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DOI: 10.4230/LIPIcs.SoCG.2017.47
URN: urn:nbn:de:0030-drops-71926
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7192/
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Keszegh, Balázs ; Pálvölgyi, Dömötör

Proper Coloring of Geometric Hypergraphs

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LIPIcs-SoCG-2017-47.pdf (0.8 MB)


Abstract

We study whether for a given planar family F there is an m such that any finite set of points can be 3-colored such that any member of F that contains at least m points contains two points with different colors. We conjecture that if F is a family of pseudo-disks, then m=3 is sufficient. We prove that when F is the family of all homothetic copies of a given convex polygon, then such an m exists. We also study the problem in higher dimensions.

BibTeX - Entry

@InProceedings{keszegh_et_al:LIPIcs:2017:7192,
  author =	{Bal{\'a}zs Keszegh and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi},
  title =	{{Proper Coloring of Geometric Hypergraphs}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{47:1--47:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7192},
  URN =		{urn:nbn:de:0030-drops-71926},
  doi =		{10.4230/LIPIcs.SoCG.2017.47},
  annote =	{Keywords: discrete geometry, decomposition of multiple coverings, geometric hypergraph coloring}
}

Keywords: discrete geometry, decomposition of multiple coverings, geometric hypergraph coloring
Seminar: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 08.06.2017


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