On the maximum number of edges in topological graphs with no four pairwise crossing edges

Abstract

A topological graph is called k -quasi-planar if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k=4. © 2009 Springer Science+Business Media, LLC.