Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles
Random Structures & Algorithms - Proceedings of the Thirteenth International Conference “Random Structures and Algorithms” held May 28–June 1, 2007, Tel Aviv, Israel
Coloring Geometric Range Spaces
Discrete & Computational Geometry
Conflict-Free Coloring for Rectangle Ranges Using O(n .382) Colors
Discrete & Computational Geometry
Proceedings of the twenty-eighth annual symposium on Computational geometry
| Hi-index | 0.00 |
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(n^0^.^3^6^8) colors always suffice, and @W(logn/log^2logn) 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(logn) colors such that every axis-parallel rectangle that contains at least three points from P is non-monochromatic.