Two floor building needing eight colors
Combinatorics
2014-05-27 v1
Abstract
Motivated by frequency assignment in office blocks, we study the chromatic number of the adjacency graph of -dimensional parallelepiped arrangements. In the case each parallelepiped is within one floor, a direct application of the Four-Colour Theorem yields that the adjacency graph has chromatic number at most . We provide an example of such an arrangement needing exactly colours. We also discuss bounds on the chromatic number of the adjacency graph of general arrangements of -dimensional parallelepipeds according to geometrical measures of the parallelepipeds (side length, total surface or volume).
Cite
@article{arxiv.1405.6620,
title = {Two floor building needing eight colors},
author = {Stéphane Bessy and Daniel Gonçalves and Jean-Sébastien Sereni},
journal= {arXiv preprint arXiv:1405.6620},
year = {2014}
}