Octants are Cover Decomposable into Many Coverings

Keszegh, Balázs and Pálvölgyi, Dömötör (2014) Octants are Cover Decomposable into Many Coverings. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 47 (5). pp. 585-588. ISSN 0925-7721

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Abstract

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.

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