An upper bound for the chromatic number of line graphs

Andrew D. King 1 Bruce A. Reed 1 Adrian R. Vetta 1
1 School of Computer Science [Montréal]
Abstract : It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $χ (G)$ is bounded above by $\lceil Δ (G) +1 + ω (G) / 2\rceil$ , where $Δ (G)$ and $ω (G)$ are the maximum degree and clique number of $G$, respectively. In this paper we prove that this bound holds if $G$ is the line graph of a multigraph. The proof yields a polynomial time algorithm that takes a line graph $G$ and produces a colouring that achieves our bound.
Keywords : line graph chromatic number
Type de document :
Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.151-156, 2005, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01184357
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 14 août 2015 - 11:37:13
Dernière modification le : jeudi 7 février 2019 - 16:56:56
Document(s) archivé(s) le : dimanche 15 novembre 2015 - 10:59:33

Fichier

dmAE0130.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01184357, version 1

Collections

INSMI | TDS-MACS

Citation

Andrew D. King, Bruce A. Reed, Adrian R. Vetta. An upper bound for the chromatic number of line graphs. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.151-156, 2005, DMTCS Proceedings. 〈hal-01184357〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

184

Téléchargements de fichiers

272

Contact


archive-ouverte@inria.fr