Octants are Cover-Decomposable into Many Coverings
Combinatorics
2012-07-04 v1 Discrete Mathematics
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.
Cite
@article{arxiv.1207.0672,
title = {Octants are Cover-Decomposable into Many Coverings},
author = {Balázs Keszegh and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1207.0672},
year = {2012}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1101.3773