{
  "id": "1006.2493",
  "version": "v1",
  "published": "2010-06-12T21:25:05.000Z",
  "updated": "2010-06-12T21:25:05.000Z",
  "title": "Diameter Bounds for Planar Graphs",
  "authors": [
    "Radoslav Fulek",
    "Filip Morić",
    "David Pritchard"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method, we begin by proving the simpler related upper bounds (4(V-1)-E)/3 and 4V^2/3E on the diameter (for connected planar graphs), which are also tight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-12T21:25:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diameter bounds",
      "connected planar graph",
      "inverse degree",
      "crucial surgery method",
      "simpler related upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.2493F"
    }
  }
}