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Colorful Strips Greg Aloupis

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
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 axis-aligned strip containing sufficiently many
points contains all colors. We show that if the strip contains at least
2k-1 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 axis-aligned strips so that any sufficiently covered point in the plane
is covered by k colors. We show that in dimension d the required


Source: Aloupis, Greg - Département d'Informatique, Université Libre de Bruxelles


Collections: Mathematics; Computer Technologies and Information Sciences