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Quantitative Restrictions on Crossing Patterns

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Beyond Planar Graphs

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Abstract

This chapter is dedicated to beyond-planar graphs defined in terms of quantitative restrictions on the intersection pattern of edges. These classes include k-planar graph, k-quasiplanar graphs, k-gap-planar graphs, and k-locally planar graphs. The chapter reviews typical proof techniques, upper and lower bounds on the number of edges in these classes, as well as recent results on containment relations between these classes, and concludes with a collection of open problems.

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Acknowledgements

We thank Yusuke Suzuki for many helpful comments on an earlier version of this chapter. Work on this survey was supported in part by the NSF awards CCF-1422311, CCF-1423615, and DMS-1800734.

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    Csaba D. Tóth

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Tóth, C.D. (2020). Quantitative Restrictions on Crossing Patterns. In: Hong, SH., Tokuyama, T. (eds) Beyond Planar Graphs. Springer, Singapore. https://doi.org/10.1007/978-981-15-6533-5_2

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