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.
Simple k-planar graphs are simple (k + 1)-quasiplanar
Didimo W.;Liotta G.;Montecchiani F.;
2020
Abstract
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.File in questo prodotto:
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