Octants are Cover Decomposable
Combinatorics
2015-03-17 v2 Discrete Mathematics
Abstract
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 open triangles can be decomposed into two coverings. However, we exhibit an indecomposable 3-fold covering.
Cite
@article{arxiv.1101.3773,
title = {Octants are Cover Decomposable},
author = {Balázs Keszegh and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1101.3773},
year = {2015}
}