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.
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Ackerman, E. On the Maximum Number of Edges in Topological Graphs with no Four Pairwise Crossing Edges. Discrete Comput Geom 41, 365–375 (2009). https://doi.org/10.1007/s00454-009-9143-9
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DOI: https://doi.org/10.1007/s00454-009-9143-9