Pascal Ochem - Negative results on acyclic improper colorings

dmtcs:3441 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3441
Negative results on acyclic improper coloringsConference paper

Authors: Pascal Ochem ORCID1

  • 1 Laboratoire Bordelais de Recherche en Informatique

Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number k is at most k2k1. We prove that this bound is tight for k3. We also show that some improper and/or acyclic colorings are NP-complete on a class C of planar graphs. We try to get the most restrictive conditions on the class C, such as having large girth and small maximum degree. In particular, we obtain the NP-completeness of 3-ACYCLIC COLORABILITY on bipartite planar graphs with maximum degree 4, and of 4-ACYCLIC COLORABILITY on bipartite planar graphs with maximum degree 8.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: NP-completeness,acyclic colorings,oriented colorings,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]

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