In a coloring of a set of points P with respect to a family of geometric regions one requires that in every region containing at least two points from P, not all the points are of the same color. Perhaps the most notorious open case is coloring of n points in the plane with respect to axis-parallel rectangles, for which it is known that O(n0.368) colors always suffice, and Ω(logn/log2logn) colors are sometimes necessary.In this note we give a simple proof showing that every set P of n points in the plane can be colored with O(log. n) colors such that every axis-parallel rectangle that contains at least three points from P is non-monochromatic.
Bibliographical noteFunding Information:
E-mail addresses: firstname.lastname@example.org (E. Ackerman), email@example.com (R. Pinchasi). 1 Supported by BSF grant (grant No. 2008290).
- Coloring geometric hypergraphs
- Conflict-free coloring
- K-Colorful coloring
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics