English

On almost-planar graphs

Combinatorics 2016-03-09 v1

Abstract

A nonplanar graph G is called almost-planar if for every edge e of G, at least one of G\e and G/e is planar. In 1990, Gubser characterized 3-connected almost-planar graphs in his dissertation. However, his proof is so long that only a small portion of it was published. The main purpose of this paper is to provide a short proof of this result. We also discuss the structure of almost-planar graphs that are not 3-connected.

Keywords

Cite

@article{arxiv.1603.02310,
  title  = {On almost-planar graphs},
  author = {Guoli Ding and Joshua Fallon and Emily Marshall},
  journal= {arXiv preprint arXiv:1603.02310},
  year   = {2016}
}

Comments

10 pages, 5 figures

R2 v1 2026-06-22T13:05:49.110Z