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Two-Planar Graphs Are Quasiplanar (1705.05569v2)
Published 16 May 2017 in cs.CG, cs.DM, and math.CO
Abstract: It is shown that every 2-planar graph is quasiplanar, that is, if a simple graph admits a drawing in the plane such that every edge is crossed at most twice, then it also admits a drawing in which no three edges pairwise cross. We further show that quasiplanarity is witnessed by a simple topological drawing, that is, any two edges cross at most once and adjacent edges do not cross.