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

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2017
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Bekos, Michael A.
Grilli, Luca
Hong, Seok-Hee
Kaufmann, Michael
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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.

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Fan-planar graphs, Beyond planarity, Graph drawing
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ISO 690BEKOS, Michael A., Sabine CORNELSEN, Luca GRILLI, Seok-Hee HONG, Michael KAUFMANN, 2017. On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs. In: Algorithmica. 2017, 79(2), pp. 401-427. ISSN 0178-4617. eISSN 1432-0541. Available under: doi: 10.1007/s00453-016-0200-5
BibTex
@article{Bekos2017-10Recog-40478,
  year={2017},
  doi={10.1007/s00453-016-0200-5},
  title={On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs},
  number={2},
  volume={79},
  issn={0178-4617},
  journal={Algorithmica},
  pages={401--427},
  author={Bekos, Michael A. and Cornelsen, Sabine and Grilli, Luca and Hong, Seok-Hee and Kaufmann, Michael}
}
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