\input zb-basic
\input zb-ioport
\iteman{io-port 06084814}
\itemau{Keszegh, Bal\'azs}
\itemti{Coloring half-planes and bottomless rectangles.}
\itemso{Comput. Geom. 45, No. 9, 495-507 (2012).}
\itemab
Summary: 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.
\itemrv{~}
\itemcc{}
\itemut{proper hypergraph coloring; geometric hypergraph; conflict-free coloring; half-plane; axis-parallel rectangle}
\itemli{doi:10.1016/j.comgeo.2011.09.004}
\end