 
Summary: Colorful Strips
Greg Aloupis
Jean Cardinal
S´ebastien Collette
Shinji Imahori
Matias Korman
Stefan Langerman §
Oded Schwartz¶
Shakhar Smorodinsky Perouz Taslakian
April 8, 2011
Abstract
We study the following geometric hypergraph coloring problem:
given a planar point set and an integer k, we wish to color the points
with k colors so that any axisaligned strip containing sufficiently many
points contains all colors. We show that if the strip contains at least
2k1 points, such a coloring can always be found. In dimension d, we
show that the same holds provided the strip contains at least k(4 ln k+
ln d) points. We also consider the dual problem of coloring a given set
of axisaligned strips so that any sufficiently covered point in the plane
is covered by k colors. We show that in dimension d the required
