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

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 kquasi-planar graph on n vertices is O(n). We provide an affirmative answer to the case k = 4.

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Eyal Ackerman
• Keywords: COMPGEOM 2006, Maximum Number, Pairwise Crossing Edges, Topological Graph