Algorithmica

, Volume 79, Issue 2, pp 401–427 | Cite as

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

  • Michael A. Bekos
  • Sabine Cornelsen
  • Luca Grilli
  • Seok-Hee Hong
  • Michael Kaufmann
Article
  • 156 Downloads

Abstract

Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a linear-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-complete, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given.

Keywords

Fan-planar graphs Beyond planarity Graph drawing 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Sabine Cornelsen
    • 2
  • Luca Grilli
    • 3
  • Seok-Hee Hong
    • 4
  • Michael Kaufmann
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany
  3. 3.Dipartimento di IngegneriaUniversità degli Studi di PerugiaPerugiaItaly
  4. 4.School of Information TechnologiesUniversity of SydneySydneyAustralia

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