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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.

Keywords

Complexity Result Combinatorial Property Outer Face Geometric Graph Outerplanar Graph 
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 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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