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.

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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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