Covering the plane with convex polygons
Discrete & Computational Geometry
Multiple Coverings of the Plane with Triangles
Discrete & Computational Geometry
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Decomposition of multiple coverings into many parts
Computational Geometry: Theory and Applications
Coloring Axis-Parallel Rectangles
Computational Geometry and Graph Theory
Decomposition of multiple coverings into more parts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Coloring geometric range spaces
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Notes: Coloring axis-parallel rectangles
Journal of Combinatorial Theory Series A
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Cover-decomposition and polychromatic numbers
ESA'11 Proceedings of the 19th European conference on Algorithms
Polychromatic coloring for half-planes
Journal of Combinatorial Theory Series A
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Polychromatic coloring for half-planes
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Coloring half-planes and bottomless rectangles
Computational Geometry: Theory and Applications
Coloring planar homothets and three-dimensional hypergraphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Coloring planar homothets and three-dimensional hypergraphs
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
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We prove that for every k 1, there exist k-fold coverings of the plane (1) with strips, (2) with axis-parallel rectangles, and (3) with homothets of any fixed concave quadrilateral, that cannot be decomposed into two coverings. We also construct, for every k 1, a set of points P and a family of disks D in the plane, each containing at least k elements of P, such that no matter how we color the points of P with two colors, there exists a disk D ∈ D, all of whose points are of the same color.