More on Decomposing Coverings by Octants
Combinatorics
2015-11-18 v2 Discrete Mathematics
Abstract
In this note we improve our upper bound given earlier by showing that every 9-fold covering of a point set in the space by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering that does not decompose into two coverings. The same bounds also hold for coverings of points in by finitely many homothets or translates of a triangle. We also prove that certain dynamic interval coloring problems are equivalent to the above question.
Cite
@article{arxiv.1503.01669,
title = {More on Decomposing Coverings by Octants},
author = {Balázs Keszegh and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1503.01669},
year = {2015}
}