Coloring Axis-Parallel Rectangles

  • Authors:
  • János Pach;Gábor Tardos

  • Affiliations:
  • CUNY and Courant Institute, City College, New York, USA;Department of Computer Science, Simon Fraser University, Burnaby, Canada

  • Venue:
  • Computational Geometry and Graph Theory
  • Year:
  • 2008

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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 [S06].