A Simplified Proof for the Edge-Density of 4-Planar Graphs
Abstract
A graph on n 3 vertices drawn in the plane such that each edge is crossed at most four times has at most 6(n-2) edges -- this result, proven by Ackerman, is outstanding in the literature of beyond-planar graphs with regard to its tightness and the structural complexity of the graph class. We provide a much shorter proof while at the same time relaxing the conditions on the graph and its embedding, i.e., allowing multi-edges and non-simple drawings.
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