Facial non-repetitive edge-colouring of plane graphs - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Journal of Graph Theory Année : 2011

Facial non-repetitive edge-colouring of plane graphs

Résumé

A sequence r1, r2, ..., r2n such that ri=rn+ i for all 1≤i≤n is called a repetition. A sequence S is called non-repetitive if no block (i.e. subsequence of consecutive terms of S) is a repetition. Let G be a graph whose edges are colored. A trail is called non-repetitive if the sequence of colors of its edges is non-repetitive. If G is a plane graph, a facial non-repetitive edge-coloring of G is an edge-coloring such that any facial trail (i.e. a trail of consecutive edges on the boundary walk of a face) is non-repetitive. We denote π′f(G) the minimum number of colors of a facial non-repetitive edge-coloring of G. In this article, we show that π′f(G)≤8 for any plane graph G. We also get better upper bounds for π′f(G) in the cases when G is a tree, a plane triangulation, a simple 3-connected plane graph, a hamiltonian plane graph, an outerplanar graph or a Halin graph. The bound 4 for trees is tight.
Fichier principal
Vignette du fichier
nonrepet-soumis.pdf (159.04 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

inria-00638439 , version 1 (23-10-2016)

Identifiants

Citer

Frédéric Havet, Stanislav Jendrol', Roman Sotak, Erika Skrabulakova. Facial non-repetitive edge-colouring of plane graphs. Journal of Graph Theory, 2011, 66 (1), pp.38--48. ⟨10.1002/jgt.20488⟩. ⟨inria-00638439⟩
125 Consultations
128 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More