Two-Planar Graphs Are Quasiplanar
arXiv:1705.05569
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.
Superseded by arXiv:1909.00223 as a result of merging with arXiv:1702.08716