{
  "id": "1308.4321",
  "version": "v1",
  "published": "2013-08-20T14:38:17.000Z",
  "updated": "2013-08-20T14:38:17.000Z",
  "title": "On Obstacle Numbers",
  "authors": [
    "Vida Dujmović",
    "Pat Morin"
  ],
  "categories": [
    "math.CO",
    "cs.CG",
    "cs.DM"
  ],
  "abstract": "The obstacle number is a new graph parameter introduced by Alpert, Koch, and Laison (2010). Mukkamala etal (2012) show that there exist graphs with n vertices having obstacle number in Omega(n/\\log n). In this note, we up this lower bound to Omega(n/(\\log\\log n)^2. Our proof makes use of an upper bound of Mukkamala etal on the number of graphs having obstacle number at most h in such a way that any subsequent improvements to their upper bound will improve our lower bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-20T14:38:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "obstacle number",
      "mukkamala etal",
      "lower bound",
      "upper bound",
      "graph parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4321D"
    }
  }
}