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}
}
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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Upper Bounds of Chromatic Functions of Graphs

  • A. V. Kostochka
  • PhD thesis, University of Novosibirsk (in Russian…
  • 1978
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