Fan-Planar Graphs: Combinatorial Properties and Complexity Results

  • Carla Binucci
  • Emilio Di Giacomo
  • Walter Didimo
  • Fabrizio Montecchiani
  • Maurizio Patrignani
  • Ioannis G. Tollis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. Fan-planar drawings have been recently introduced by Kaufmann and Ueckerdt, who proved that every n-vertex fan-planar drawing has at most 5n − 10 edges, and that this bound is tight for n ≥ 20. We extend their result from both the combinatorial and the algorithmic point of view. We prove tight bounds on the density of constrained versions of fan-planar drawings and study the relationship between fan-planarity and k-planarity. Also, we prove that testing fan-planarity in the variable embedding setting is NP-complete.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Carla Binucci
    • 1
  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Fabrizio Montecchiani
    • 1
  • Maurizio Patrignani
    • 2
  • Ioannis G. Tollis
    • 3
  1. 1.Università degli Studi di PerugiaItaly
  2. 2.Università Roma TreItaly
  3. 3.Univ. of Crete and Institute of Computer Science-FORTHGreece

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