Coloring Points with Respect to Squares

Eyal Ackerman, Balázs Keszegh, Mate Vizer

Research output: Contribution to journalArticlepeer-review


We consider the problem of 2-coloring geometric hypergraphs. Specifically, we show that there is a constant m such that any finite set of points in the plane S⊂ R2 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 2-coloring points with respect to homothets of a fixed parallelogram.

Original languageEnglish
Pages (from-to)757-784
Number of pages28
JournalDiscrete and Computational Geometry
Issue number4
StatePublished - 1 Dec 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media New York.


  • Cover-decomposability
  • Geometric hypergraph coloring
  • Self-coverability

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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