Local chromatic number and topology

Gábor Simonyi 1 Gábor Tardos 1
1 Alfréd Rényi Institute of Mathematics
Abstract : The local chromatic number of a graph, introduced by Erdős et al., is the minimum number of colors that must appear in the closed neighborhood of some vertex in any proper coloring of the graph. This talk would like to survey some of our recent results on this parameter. We give a lower bound for the local chromatic number in terms of the lower bound of the chromatic number provided by the topological method introduced by Lovász. We show that this bound is tight in many cases. In particular, we determine the local chromatic number of certain odd chromatic Schrijver graphs and generalized Mycielski graphs. We further elaborate on the case of $4$-chromatic graphs and, in particular, on surface quadrangulations.
Keywords : graph coloring topological method Schrijver graphs Mycielski graphs surface quadrangulation
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.375-378, 2005, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger
https://hal.inria.fr/hal-01184436
Contributeur : Coordination Episciences Iam <>
Soumis le : vendredi 14 août 2015 - 14:58:48
Dernière modification le : jeudi 11 mai 2017 - 01:02:52
Document(s) archivé(s) le : dimanche 15 novembre 2015 - 11:11:54

Fichier

dmAE0172.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01184436, version 1

Collections

INSMI | TDS-MACS

Citation

Gábor Simonyi, Gábor Tardos. Local chromatic number and topology. 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.375-378, 2005, DMTCS Proceedings. 〈hal-01184436〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

330

Téléchargements de fichiers

148

Contact


archive-ouverte@inria.fr