Simple k-planar graphs are simple (k + 1)-quasiplanar

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.