InforLorV4, Main, Exploration, bibRecord, 000666

Two floor building needing eight colors

Identifieur interne : 000666 ( Main/Exploration ); précédent : 000665; suivant : 000667

Two floor building needing eight colors

Auteurs : Stéphane Bessy [France] ; Daniel Gonçalves [France] ; Jean-Sébastien Sereni [France]

Source :

Journal of Graph Algorithms and Applications (JGAA) [ 1526-1719 ] ; 2015-01.

RBID : Hal:hal-00996709

English descriptors

mix :
- WLAN, adjacency, cuboids, graph colouring, parallelepiped arrangements.

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).

Url:

https://hal.archives-ouvertes.fr/hal-00996709

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 005005
to stream Hal, to step Curation: 005005
to stream Hal, to step Checkpoint: 000649
to stream Main, to step Merge: 000670
to stream Main, to step Curation: 000666

Le document en format XML

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<front><div type="abstract" xml:lang="en">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).</div>
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<name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000666 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000666 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     Hal:hal-00996709
   |texte=   Two floor building needing eight colors
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur la recherche en informatique en Lorraine

Two floor building needing eight colors

Two floor building needing eight colors

Source :

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri