Abstract : For any graph $G$, the $k$-improper chromatic number $\chi^k(G)$ is the smallest number of colours used in a colouring of $G$ such that each colour class induces a subgraph of maximum degree $k$. We investigate the ratio of the $k$-improper chromatic number to the clique number for unit disk graphs and random unit disk graphs to generalise results where only proper colouring was considered.
https://hal.inria.fr/inria-00070259
Contributeur : Rapport de Recherche Inria
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Soumis le : vendredi 19 mai 2006 - 19:45:53
Dernière modification le : mercredi 31 janvier 2018 - 10:24:04
Document(s) archivé(s) le : dimanche 4 avril 2010 - 20:46:08
Ross J. Kang, Tobias Müller, Jean-Sébastien Sereni. Improper colouring of (random) unit disk graphs. [Research Report] RR-5761, INRIA. 2005, pp.18. 〈inria-00070259〉
