Negative results on acyclic improper colorings
نویسنده
چکیده
Raspaud and Sopena showed that the oriented chromatic number of a graph with acyclic chromatic number k is at most k2. We prove that this bound is tight for k ≥ 3. We also consider acyclic improper colorings on planar graphs and partial ktrees. Finally, we show that some improper and/or acyclic colorings are NP-complete on restricted subclasses of planar graphs, in particular acyclic 3-colorability on bipartite planar graphs with maximum degree 4, and acyclic 4-colorability on bipartite planar graphs with maximum degree 8.
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