Covering the plane with convex polygons
Discrete & Computational Geometry
Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
The Minimum Independence Number of a Hasse Diagram
Combinatorics, Probability and Computing
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Conflict-free coloring for rectangle ranges using O(n.382) colors
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
On The Chromatic Number of Geometric Hypergraphs
SIAM Journal on Discrete Mathematics
Multiple Coverings of the Plane with Triangles
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
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Coloring geometric range spaces
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
The potential to improve the choice: list conflict-free coloring for geometric hypergraphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Tight lower bounds for the size of epsilon-nets
Proceedings of the twenty-seventh annual symposium on Computational geometry
Conflict-Free coloring made stronger
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Coloring half-planes and bottomless rectangles
Computational Geometry: Theory and Applications
Coloring hypergraphs induced by dynamic point sets and bottomless rectangles
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by precisely r members of the family, all of which have the same color. For r=2, this answers a question of S. Smorodinsky [S. Smorodinsky, On the chromatic number of some geometric hypergraphs, SIAM J. Discrete Math. 21 (2007) 676-687].