Discrete & Computational Geometry

, Volume 34, Issue 1, pp 47–70

Conflict-Free Coloring of Points and Simple Regions in the Plane


DOI: 10.1007/s00454-005-1162-6

Cite this article as:
Har-Peled, S. & Smorodinsky, S. Discrete Comput Geom (2005) 34: 47. doi:10.1007/s00454-005-1162-6


We study conflict-free colorings, where the underlying set systems arise in geometry. Our main result is a general framework for conflict-free coloring of regions with low union complexity. A coloring of regions is conflict-free if for any covered point in the plane, there exists a region that covers it with a unique color (i.e., no other region covering this point has the same color). For example, we show that we can conflict-free color any family of n pseudo-discs with O(log n) colors.

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Computer Science, University of Illinois, 201 N. Goodwin Avenue, Urbana, IL 61801USA
  2. 2.Institute for Theoretische Informatik, ETH Zurich, IFW CH-8092, ZurichSwitzerland