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On Embedding a Cycle in a Plane Graph

(Extended Abstract)
  • Pier Francesco Cortese
  • Giuseppe Di Battista
  • Maurizio Patrignani
  • Maurizio Pizzonia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)

Abstract

Consider a planar drawing \({\it \Gamma}\) of a planar graph G such that the vertices are drawn as small circles and the edges are drawn as thin strips. Consider a cycle c of G. Is it possible to draw c as a non-intersecting closed curve inside \({\it \Gamma}\), following the circles that correspond in \({\it \Gamma}\) to the vertices of c and the strips that connect them? We show that this test can be done in polynomial time and study this problem in the framework of clustered planarity for highly non-connected clustered graphs.

Keywords

Polynomial Time Plane Graph Cluster Expansion Underlying Graph Planar Partition 
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 2006

Authors and Affiliations

  • Pier Francesco Cortese
    • 1
  • Giuseppe Di Battista
    • 1
  • Maurizio Patrignani
    • 1
  • Maurizio Pizzonia
    • 1
  1. 1.Università Roma Tre 

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