Coloring points with respect to squares

Eyal Ackerman, Balázs Keszegh, Máté Vizer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publication32nd International Symposium on Computational Geometry, SoCG 2016
EditorsSandor Fekete, Anna Lubiw
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770095
StatePublished - 1 Jun 2016
Event32nd International Symposium on Computational Geometry, SoCG 2016 - Boston, United States
Duration: 14 Jun 201617 Jun 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference32nd International Symposium on Computational Geometry, SoCG 2016
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© Eyal Ackerman, Balázs Keszegh, and Máté Vizer.


  • Cover-decomposability
  • Geometric hypergraph coloring
  • Homothets
  • Polychromatic coloring

ASJC Scopus subject areas

  • Software


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