Two floor building needing eight colors - Archive ouverte HAL
Article Dans Une Revue Journal of Graph Algorithms and Applications Année : 2015

Two floor building needing eight colors

Stéphane Bessy
Jean-Sébastien Sereni
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  • IdRef : 110354540

Résumé

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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Dates et versions

hal-00996709 , version 1 (26-05-2014)
hal-00996709 , version 2 (07-01-2016)

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Stéphane Bessy, Daniel Gonçalves, Jean-Sébastien Sereni. Two floor building needing eight colors. Journal of Graph Algorithms and Applications, 2015, 19 (1), pp.1--9. ⟨10.7155/jgaa.00344⟩. ⟨hal-00996709v2⟩
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