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Fan-Planar Graphs

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Abstract

A fan-planar graph is a graph that admits a drawing, in which each edge can cross only edges with a common endvertex, and this endvertex is on the same side of the edge. Hence, by definition, fan-planar graphs extend the class of 1-planar graphs, but still form a proper subclass of 3-quasiplanar graphs, as they cannot contain three mutually crossing edges. Similarly to several other classes of beyond-planar graphs, fan-planar graphs have a linear number of edges, it is NP-hard to recognize them (both in general and in the fixed rotation system setting), while polynomial-time recognition and drawing algorithms are known only for special variants of them. In this chapter, we review known combinatorial and algorithmic results on fan-planar graphs and we identify several open problems in the field.

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Acknowledgements

The authors’ research was supported in part by the DFG grant KA812/18-1 and by the scientific project: “Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni” - Ricerca di Base 2017, Dipartimento di Ingegneria dell’Università degli Studi di Perugia.

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Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Tübingen, Germany

    Michael A. Bekos

  2. Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy

    Luca Grilli

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  1. Michael A. Bekos
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  2. Luca Grilli
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Correspondence to Luca Grilli .

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Editors and Affiliations

  1. School of Computer Science, University of Sydney, Sydney, NSW, Australia

    Seok-Hee Hong

  2. School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo, Japan

    Takeshi Tokuyama

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Bekos, M.A., Grilli, L. (2020). Fan-Planar Graphs. In: Hong, SH., Tokuyama, T. (eds) Beyond Planar Graphs. Springer, Singapore. https://doi.org/10.1007/978-981-15-6533-5_8

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  • DOI: https://doi.org/10.1007/978-981-15-6533-5_8

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-6532-8

  • Online ISBN: 978-981-15-6533-5

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