Coloring hypergraphs induced by dynamic point sets and bottomless rectangles
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Octants are cover-decomposable into many coverings
Computational Geometry: Theory and Applications
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We prove that octants are cover-decomposable; i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into two coverings. We also show that any 12-fold covering of the whole plane with the translates of a given open triangle can be decomposed into two coverings. However, we exhibit an indecomposable 3-fold covering with translates of a given triangle.