Acyclically 3-Colorable Planar Graphs

  • Patrizio Angelini
  • Fabrizio Frati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)


In this paper we study the planar graphs that admit an acyclic 3-coloring. We show that testing acyclic 3-colorability is \(\cal NP\)-hard 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 is acyclically 3-colorable. Finally, we characterize the series-parallel graphs such that every 3-coloring is acyclic and we provide a linear-time recognition algorithm for such graphs.


Planar Graph Parallel Composition Simple Cycle Outerplanar Graph Biconnected Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Fabrizio Frati
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneRoma Tre University 

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