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arXiv · 1909.00223

Simple $k$-Planar Graphs are Simple $(k+1)$-Quasiplanar

Patrizio Angelini·Michael A. Bekos·Franz J. Brandenburg·Giordano Da Lozzo·Giuseppe Di Battista·Walter Didimo·Michael Hoffmann·Giuseppe Liotta·Fabrizio Montecchiani·Ignaz Rutter·Csaba D. Tóth
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Abstract

A simple topological graph is $k$-quasiplanar ($k\geq 2$) if it contains no $k$ pairwise crossing edges, and $k$-planar if no edge is crossed more than $k$ times. In this paper, we explore the relationship between $k$-planarity and $k$-quasiplanarity to show that, for $k \geq 2$, every $k$-planar simple topological graph can be transformed into a $(k+1)$-quasiplanar simple topological graph.

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Patrizio Angelini, Michael A. Bekos, Franz J. Brandenburg, Giordano Da Lozzo, Giuseppe Di Battista, Walter Didimo, Michael Hoffmann, Giuseppe Liotta, Fabrizio Montecchiani, Ignaz Rutter, Csaba D. Tóth. 2019-08-31. Simple $k$-Planar Graphs are Simple $(k+1)$-Quasiplanar. https://doi.org/10.1016/j.jctb.2019.08.006

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