On the Maximum Number of Edges in Topological Graphs with no Four Pairwise Crossing Edges

Authors:
Eyal Ackerman
Affiliations:
Technion—Israel Institute of Technology, Computer Science Dept., 32000, Haifa, Israel
Venue:
Discrete & Computational Geometry
Year:
2009

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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.