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Acyclically 3-Colorable Planar Graphs

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

Abstract

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.

Keywords

Planar Graph Parallel Composition Simple Cycle Outerplanar Graph Biconnected Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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