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
Go to the corresponding LIPIcs Volume Portal

Ackerman, Eyal ; Keszegh, Balázs ; Vizer, Máté

Coloring Points with Respect to Squares

LIPIcs-SoCG-2016-5.pdf (0.6 MB)


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

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-58972},
  doi =		{10.4230/LIPIcs.SoCG.2016.5},
  annote =	{Keywords: Geometric hypergraph coloring, Polychromatic coloring, Homothets, Cover-decomposability}

Keywords: Geometric hypergraph coloring, Polychromatic coloring, Homothets, Cover-decomposability
Collection: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 10.06.2016

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI