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Fan-Planar Graphs: Combinatorial Properties and Complexity Results

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,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.

Research supported in part by the MIUR project AMANDA “Algorithmics for MAssive and Networked DAta”, prot. 2012C4E3KT_001. This work started at the Bertinoro Workshop on Graph Drawing 2014. We thank Michael Kaufmann and Torsten Ueckerdt for suggesting the study of fan-planar graphs during the workshop. We also thank all the participants of the workshop for the useful discussions on this topic.

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Binucci, C., Di Giacomo, E., Didimo, W., Montecchiani, F., Patrignani, M., Tollis, I.G. (2014). Fan-Planar Graphs: Combinatorial Properties and Complexity Results. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45803-7_16

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  • DOI: https://doi.org/10.1007/978-3-662-45803-7_16

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