Octants are cover-decomposable into many coverings
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k  there is an m(k) m ( k ) such that any m(k) m ( k ) -fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into k  coverings. As a corollary, we obtain that any m(k) m ( k ) -fold covering of any subset of the plane with a finite number of homothetic copies of a given triangle can be decomposed into k coverings. Previously only some weaker bounds were known for related problems [20].
cover-decomposition geometric hypergraph coloring