English

The Kelmans-Seymour conjecture for apex graphs

Combinatorics 2010-12-30 v1

Abstract

We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided K5K_{_5} or a K4K^-_{_4} (= K4K_{_4} with a single edge removed) as a subgraph. Together with a recent result of Ma and Yu that {\sl every nonplanar 5-connected graph containing K4K^-_{_4} as a subgraph has a subdivided K5K_{_5}}; this settles the Kelmans-Seymour conjecture for apex graphs.

Keywords

Cite

@article{arxiv.1012.5793,
  title  = {The Kelmans-Seymour conjecture for apex graphs},
  author = {Elad Aigner-Horev and Roi Krakovski},
  journal= {arXiv preprint arXiv:1012.5793},
  year   = {2010}
}

Comments

10 pages, submitted on August 10th 2010

R2 v1 2026-06-21T17:04:53.686Z