2012/07/03 by Balázs Keszegh, Keszegh, Balázs, Dömötör Pálvölgyi +1 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Point processes and geometric inequalities
paper · doi:10.48550/arxiv.1207.0672
openalex publication_date 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k) such that any 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)-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.