On embedding a cycle in a plane graph

  • Authors:
  • Pier Francesco Cortese;Giuseppe Di Battista;Maurizio Patrignani;Maurizio Pizzonia

  • Affiliations:
  • Università Roma Tre;Università Roma Tre;Università Roma Tre;Università Roma Tre

  • Venue:
  • GD'05 Proceedings of the 13th international conference on Graph Drawing
  • Year:
  • 2005

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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.