{
  "id": "1103.5364",
  "version": "v2",
  "published": "2011-03-28T14:17:48.000Z",
  "updated": "2013-11-04T12:54:47.000Z",
  "title": "Irreducible triangulations of surfaces with boundary",
  "authors": [
    "Alexandre Boulch",
    "Éric Colin de Verdière",
    "Atsuhiro Nakamoto"
  ],
  "journal": "Graphs and Combinatorics 29(6):1675-1688, 2013",
  "doi": "10.1007/s00373-012-1244-1",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-04T12:54:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15",
      "57N05"
    ],
    "keywords": [
      "irreducible triangulation",
      "technique yields",
      "worse constant",
      "elementary"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.5364B"
    }
  }
}