English

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.

Keywords

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Superseded by arXiv:1909.00223 as a result of merging with arXiv:1702.08716

R2 v1 2026-06-22T19:48:11.780Z