{
  "id": "1103.2724",
  "version": "v1",
  "published": "2011-03-14T17:41:03.000Z",
  "updated": "2011-03-14T17:41:03.000Z",
  "title": "Lower bounds on the obstacle number of graphs",
  "authors": [
    "Padmini Mukkamala",
    "János Pach",
    "Dömötör Pálvölgyi"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Given a graph $G$, an {\\em obstacle representation} of $G$ is a set of points in the plane representing the vertices of $G$, together with a set of connected obstacles such that two vertices of $G$ are joined by an edge if and only if the corresponding points can be connected by a segment which avoids all obstacles. The {\\em obstacle number} of $G$ is the minimum number of obstacles in an obstacle representation of $G$. It is shown that there are graphs on $n$ vertices with obstacle number at least $\\Omega({n}/{\\log n})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-14T17:41:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C62",
      "05C75",
      "68R10"
    ],
    "keywords": [
      "obstacle number",
      "lower bounds",
      "obstacle representation",
      "minimum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2724M"
    }
  }
}