# Acyclically 3-colorable planar graphs

@article{Angelini2012Acyclically3P, title={Acyclically 3-colorable planar graphs}, author={Patrizio Angelini and Fabrizio Frati}, journal={J. Comb. Optim.}, year={2012}, volume={24}, pages={116-130} }

- Published 2012 in J. Comb. Optim.
DOI:10.1007/s10878-011-9385-3

In this paper we study the planar graphs that admit an acyclic 3-coloring. We show that testing acyclic 3-colorability is NP-hard, even for planar graphs of maximum degree 4, and we show that there exist infinite classes of cubic planar graphs that are not acyclically 3-colorable. Further, we show that every planar graph has a subdivision with one vertex per edge that admits an acyclic 3-coloring. Finally, we show that every series-parallel graph admits an acyclic 3-coloring and we give a… CONTINUE READING

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