English

Subdivisions in apex graphs

Combinatorics 2010-12-30 v1

Abstract

The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided K5K_{_5}. Certain questions of Mader propose a "plan" towards a possible resolution of this conjecture. One part of this plan is to show that a 5-connected nonplanar graph containing K4K^-_{_4} or K2,3K_{_{2,3}} as a subgraph has a subdivided K5K_{_5}. Recently, Ma and Yu showed that a 5-connected nonplanar graph containing K4K^-_{_4} as a subgraph has a subdivided K5K_{_5}. We take interest in K2,3K_{_{2,3}} and prove that a 5-connected nonplanar apex graph containing K2,3K_{_{2,3}} as a subgraph has a subdivided K5K_{_5}

Keywords

Cite

@article{arxiv.1012.5792,
  title  = {Subdivisions in apex graphs},
  author = {Elad Aigner-Horev},
  journal= {arXiv preprint arXiv:1012.5792},
  year   = {2010}
}

Comments

30 pages, 3 figures, submitted on June 26th 2010

R2 v1 2026-06-21T17:04:53.392Z