Clustering Cycles into Cycles of Clusters

  • Pier Francesco Cortese
  • Giuseppe Di Battista
  • Maurizio Patrignani
  • Maurizio Pizzonia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)

Abstract

In this paper we study the clustered graphs whose underlying graph is a cycle. This is a simple family of clustered graphs that are “highly non connected”. We start by studying 3-cluster cycles, that are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case testing the c-planarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3-cluster cycles in terms of formal grammars. Finally, we generalize the results on 3-cluster cycles considering clustered graphs that at each level of the inclusion tree have a cycle structure. Even in this case we show efficient c-planarity testing and drawing algorithms.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Pier Francesco Cortese
    • 1
  • Giuseppe Di Battista
    • 1
  • Maurizio Patrignani
    • 1
  • Maurizio Pizzonia
    • 1
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly

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