TY - JOUR
AU - 
AB - Motivated by frequency assignment in office blocks, we study the chromatic number of the adjacency graph of a 3-dimensional parallelepiped arrangement. 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 colors. 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 area or volume). Submitted: Reviewed: Revised: Final: Accepted: May 2014 August 2014 September 2014 January 2015 December 2014 Published: January 2015 Article type: Communicated by: Regular paper J.S.B. Mitchell The second and third author’s work were partially supported by the French Agence Nationale de la Recherche under references ANR-12-JS02-002-01 and ANR-10-JCJC-0204-01, respectively. E-mail addresses: bessy@lirmm.fr (S. Bessy) goncalves@lirmm.fr (D. Gonçalves) sereni@kam.mff.cuni.cz (J.-S. Sereni) 2 Bessy, Gonçalves, and Sereni Two-floor buildings need eight colors 1 Introduction The Graph Colouring Problem for Office Blocks was raised by BAE Systems at the 53rd European Study Group with Industry in 2005 [1]. Consider an office complex with space rented by several independent organisations. It 
TI - Two-floor buildings need eight colors
JF - Journal of Graph Algorithms and Applications
DO - 10.7155/jgaa.00344
DA - 2015-01-01
UR - https://www.deepdyve.com/lp/unpaywall/two-floor-buildings-need-eight-colors-46j02ZXoCg
DP - DeepDyve
ER -