Coloring half-planes and bottomless rectangles

Authors:
BaláZs Keszegh
Affiliations:
Rényi Institute, Budapest, Hungary
Venue:
Computational Geometry: Theory and Applications
Year:
2012

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Abstract

We prove lower and upper bounds for the chromatic number of certain hypergraphs defined by geometric regions. This problem has close relations to conflict-free colorings. One of the most interesting type of regions to consider for this problem is that of the axis-parallel rectangles. We completely solve the problem for a special case of them, for bottomless rectangles. We also give an almost complete answer for half-planes and pose several open problems. Moreover, we give efficient coloring algorithms.