Coloring axis-parallel rectangles

János Pach, Gábor Tardos

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r=2, this answers a question of S. Smorodinsky [S. Smorodinsky, On the chromatic number of some geometric hypergraphs, SIAM J. Discrete Math. 21 (2007) 676-687].

Original languageEnglish
Pages (from-to)776-782
Number of pages7
JournalJournal of Combinatorial Theory. Series A
Volume117
Issue number6
DOIs
Publication statusPublished - Aug 2010

Keywords

  • Chromatic number
  • Coloring
  • Hypergraph

ASJC Scopus subject areas

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

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