Abstract
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.
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Har-Peled, S., Smorodinsky, S. Conflict-Free Coloring of Points and Simple Regions in the Plane. Discrete Comput Geom 34, 47–70 (2005). https://doi.org/10.1007/s00454-005-1162-6
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DOI: https://doi.org/10.1007/s00454-005-1162-6