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Splitting Clusters to Get C-Planarity

  • Patrizio Angelini
  • Fabrizio Frati
  • Maurizio Patrignani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)

Abstract

In this paper we introduce a generalization of the c-planarity testing problem for clustered graphs. Namely, given a clustered graph, the goal of the Split-C-Planarity problem is to split as few clusters as possible in order to make the graph c-planar. Determining whether zero splits are enough coincides with testing c-planarity. We show that Split-C-Planarity is NP-complete for c-connected clustered triangulations and for non-c-connected clustered paths and cycles. On the other hand, we present a polynomial-time algorithm for flat c-connected clustered graphs whose underlying graph is a biconnected series-parallel graph, both in the fixed and in the variable embedding setting, when the splits are assumed to maintain the c-connectivity of the clusters.

Keywords

Satisfying Condition Input Graph Parallel Composition Truth Assignment Outer Face 
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
  • Maurizio Patrignani
    • 1
  1. 1.Università Roma Tre 

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