{
  "id": "1308.6717",
  "version": "v1",
  "published": "2013-08-30T11:58:45.000Z",
  "updated": "2013-08-30T11:58:45.000Z",
  "title": "Hamiltonian Cycle in Semi-Equivelar Maps on the Torus",
  "authors": [
    "Dipendu Maity",
    "Ashish Kumar Upadhyay"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types $\\{3^{3},4^{2}\\}$, $\\{3^{2},4,3,4\\}$, $\\{6,3,6,3\\}$, $\\{3^{4},6\\}$, $\\{4,8^{2}\\}$, $\\{3,12^{2}\\}$, $\\{4,6,12\\}$, $\\{6,4,3,4\\}$ exist on the torus. In this article we show the existence of Hamiltonian cycle in each semi-equivelar map on the torus except the map of type $\\{3,12^{2}\\}$. This result gives the partial solution to the conjecture which is given by Gr$\\ddot{u}$nbaum \\cite{grunbaum} and Nash-Williams \\cite{nash williams} that every 4-connected graph on the torus is Hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-30T11:58:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B70",
      "05C45",
      "52C38",
      "G.2.2"
    ],
    "keywords": [
      "semi-equivelar map",
      "hamiltonian cycle",
      "archimedean solids",
      "partial solution",
      "generalizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.6717M"
    }
  }
}