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arXiv · 1405.6620

Two floor building needing eight colors

Stéphane Bessy·Daniel Gonçalves·Jean-Sébastien Sereni
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Abstract

Motivated by frequency assignment in office blocks, we study the chromatic number of the adjacency graph of $3$-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 $8$. We provide an example of such an arrangement needing exactly $8$ colours. We also discuss bounds on the chromatic number of the adjacency graph of general arrangements of $3$-dimensional parallelepipeds according to geometrical measures of the parallelepipeds (side length, total surface or volume).

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Stéphane Bessy, Daniel Gonçalves, Jean-Sébastien Sereni. 2014-05-26. Two floor building needing eight colors. https://arxiv.org/abs/1405.6620

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