{
  "id": "1012.5792",
  "version": "v1",
  "published": "2010-12-28T16:58:01.000Z",
  "updated": "2010-12-28T16:58:01.000Z",
  "title": "Subdivisions in apex graphs",
  "authors": [
    "Elad Aigner-Horev"
  ],
  "comment": "30 pages, 3 figures, submitted on June 26th 2010",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Kelmans-Seymour conjecture states that the 5-connected nonplanar graphs contain a subdivided $K_{_5}$. 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 $K^-_{_4}$ or $K_{_{2,3}}$ as a subgraph has a subdivided $K_{_5}$. Recently, Ma and Yu showed that a 5-connected nonplanar graph containing $K^-_{_4}$ as a subgraph has a subdivided $K_{_5}$. We take interest in $K_{_{2,3}}$ and prove that a 5-connected nonplanar apex graph containing $K_{_{2,3}}$ as a subgraph has a subdivided $K_{_5}$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-28T16:58:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subdivisions",
      "nonplanar graph containing",
      "nonplanar graphs contain",
      "kelmans-seymour conjecture states",
      "nonplanar apex graph containing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.5792A"
    }
  }
}