Negative results on acyclic improper colorings - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Discrete Mathematics and Theoretical Computer Science Année : 2005

Negative results on acyclic improper colorings

Résumé

Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number $k$ is at most $k2^{k-1}$. We prove that this bound is tight for $k \geq 3$. We also show that some improper and/or acyclic colorings are $\mathrm{NP}$-complete on a class $\mathcal{C}$ of planar graphs. We try to get the most restrictive conditions on the class $\mathcal{C}$, such as having large girth and small maximum degree. In particular, we obtain the $\mathrm{NP}$-completeness of $3$-$\mathrm{ACYCLIC \space COLORABILITY}$ on bipartite planar graphs with maximum degree $4$, and of $4$-$\mathrm{ACYCLIC \space COLORABILITY}$ on bipartite planar graphs with maximum degree $8$.
Fichier principal
Vignette du fichier
dmAE0169.pdf (157.81 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01184430 , version 1 (14-08-2015)

Identifiants

Citer

Pascal Ochem. Negative results on acyclic improper colorings. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.357-362, ⟨10.46298/dmtcs.3441⟩. ⟨hal-01184430⟩

Collections

CNRS TDS-MACS
91 Consultations
559 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More