Nonrepetitive colorings of graphs - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

Nonrepetitive colorings of graphs

Résumé

A vertex coloring of a graph $G$ is $k \textit{-nonrepetitive}$ if one cannot find a periodic sequence with $k$ blocks on any simple path of $G$. The minimum number of colors needed for such coloring is denoted by $\pi _k(G)$ . This idea combines graph colorings with Thue sequences introduced at the beginning of 20th century. In particular Thue proved that if $G$ is a simple path of any length greater than $4$ then $\pi _2(G)=3$ and $\pi_3(G)=2$. We investigate $\pi_k(G)$ for other classes of graphs. Particularly interesting open problem is to decide if there is, possibly huge, $k$ such that $\pi_k(G)$ is bounded for planar graphs.
Fichier principal
Vignette du fichier
dmAE0126.pdf (101.06 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01184372 , version 1 (14-08-2015)

Identifiants

Citer

Noga Alon, Jaroslaw Grytczuk. Nonrepetitive colorings of graphs. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.133-134, ⟨10.46298/dmtcs.3415⟩. ⟨hal-01184372⟩

Collections

TDS-MACS
197 Consultations
579 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More