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.2018.52
URN: urn:nbn:de:0030-drops-87657
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8765/
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Keszegh, Balázs

Coloring Intersection Hypergraphs of Pseudo-Disks

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LIPIcs-SoCG-2018-52.pdf (0.6 MB)

Abstract

We prove that the intersection hypergraph of a family of n pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with 4 colors and a conflict-free coloring with O(log n) colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of n regions with linear union complexity with respect to a family of pseudo-disks admits a proper coloring with constantly many colors and a conflict-free coloring with O(log n) colors. Our results serve as a common generalization and strengthening of many earlier results, including ones about proper and conflict-free coloring points with respect to pseudo-disks, coloring regions of linear union complexity with respect to points and coloring disks with respect to disks.

BibTeX - Entry

@InProceedings{keszegh:LIPIcs:2018:8765,
  author =	{Bal{\'a}zs Keszegh},
  title =	{{Coloring Intersection Hypergraphs of Pseudo-Disks}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{52:1--52:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8765},
  URN =		{urn:nbn:de:0030-drops-87657},
  doi =		{10.4230/LIPIcs.SoCG.2018.52},
  annote =	{Keywords: combinatorial geometry, conflict-free coloring, geometric hypergraph coloring}
}

Keywords: combinatorial geometry, conflict-free coloring, geometric hypergraph coloring
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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