Abstract
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.
Original language | English |
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Pages (from-to) | 811-815 |
Number of pages | 5 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 120 |
Issue number | 4 |
DOIs | |
State | Published - May 2013 |
Bibliographical note
Funding Information:E-mail addresses: [email protected] (E. Ackerman), [email protected] (R. Pinchasi). 1 Supported by BSF grant (grant No. 2008290).
Keywords
- Coloring geometric hypergraphs
- Conflict-free coloring
- K-Colorful coloring
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics