Coloring half-planes and bottomless rectangles
Combinatorics
2011-05-03 v1
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.
Cite
@article{arxiv.1105.0169,
title = {Coloring half-planes and bottomless rectangles},
author = {Balázs Keszegh},
journal= {arXiv preprint arXiv:1105.0169},
year = {2011}
}