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

08/31/2019

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by   Patrizio Angelini, et al.

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A simple topological graph is k-quasiplanar (k≥ 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 ≥ 2, every k-planar simple topological graph can be transformed into a (k+1)-quasiplanar simple topological graph.