{
  "id": "1610.06558",
  "version": "v1",
  "published": "2016-10-20T19:56:50.000Z",
  "updated": "2016-10-20T19:56:50.000Z",
  "title": "Hamiltonicity of planar graphs with a forbidden minor",
  "authors": [
    "M. N. Ellingham",
    "Emily A. Marshall",
    "Kenta Ozeki",
    "Shoichi Tsuchiya"
  ],
  "comment": "18 pages, 29 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Tutte showed that $4$-connected planar graphs are Hamiltonian, but it is well known that $3$-connected planar graphs need not be Hamiltonian. We show that $K_{2,5}$-minor-free $3$-connected planar graphs are Hamiltonian. This does not extend to $K_{2,5}$-minor-free $3$-connected graphs in general, as shown by the Petersen graph, and does not extend to $K_{2,6}$-minor-free $3$-connected planar graphs, as we show by an infinite family of examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-20T19:56:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45"
    ],
    "keywords": [
      "connected planar graphs",
      "forbidden minor",
      "hamiltonicity",
      "hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}