On coloring points with respect to rectangles

Eyal Ackerman, Rom Pinchasi

Research output: Contribution to journalArticlepeer-review

Abstract

In a coloring of a set of points P with respect to a family of geometric regions one requires that in every region containing at least two points from P, not all the points are of the same color. Perhaps the most notorious open case is coloring of n points in the plane with respect to axis-parallel rectangles, for which it is known that O(n0.368) colors always suffice, and Ω(logn/log2logn) colors are sometimes necessary.In this note we give a simple proof showing that every set P of n points in the plane can be colored with O(log. n) colors such that every axis-parallel rectangle that contains at least three points from P is non-monochromatic.

Original languageEnglish
Pages (from-to)811-815
Number of pages5
JournalJournal of Combinatorial Theory. Series A
Volume120
Issue number4
DOIs
StatePublished - May 2013

Bibliographical note

Funding Information:
E-mail addresses: ackerman@sci.haifa.ac.il (E. Ackerman), room@math.technion.ac.il (R. Pinchasi). 1 Supported by BSF grant (grant No. 2008290).

Keywords

  • Coloring geometric hypergraphs
  • Conflict-free coloring
  • K-Colorful coloring

ASJC Scopus subject areas

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

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