Two-Planar Graphs Are Quasiplanar
Computational Geometry
2019-09-05 v2 Discrete Mathematics
Combinatorics
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.
Cite
@article{arxiv.1705.05569,
title = {Two-Planar Graphs Are Quasiplanar},
author = {Michael Hoffmann and Csaba D. Tóth},
journal= {arXiv preprint arXiv:1705.05569},
year = {2019}
}
Comments
Superseded by arXiv:1909.00223 as a result of merging with arXiv:1702.08716