On the Density of 3-Planar Graphs


A k-planar graph is a graph that can be drawn in the plane such that every edge is crossed at most k times. For k ≤ 4, Pach and Tóth [19] proved a bound of (k + 3)(n− 2) on the total number of edges of a k-planar graph, which is tight for k = 1, 2. For k = 3, the bound of 6n− 12 has been improved to 11 2 n− 11 in [18] and has been shown to be optimal up to… (More)


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