{
  "id": "1411.1303",
  "version": "v1",
  "published": "2014-11-04T18:05:26.000Z",
  "updated": "2014-11-04T18:05:26.000Z",
  "title": "Convex polygons in geometric triangulations",
  "authors": [
    "Adrian Dumitrescu",
    "Csaba D. Tóth"
  ],
  "comment": "19 pages, 5 figures",
  "categories": [
    "math.MG",
    "cs.DM",
    "math.CO"
  ],
  "abstract": "We show that the maximum number of convex polygons in a triangulation of $n$ points in the plane is $O(1.5029^n)$. This improves an earlier bound of $O(1.6181^n)$ established by van Kreveld, L\\\"offler, and Pach (2012) and almost matches the current best lower bound of $\\Omega(1.5028^n)$ due to the same authors. Given a planar straight-line graph $G$ with $n$ vertices, we show how to compute efficiently the number of convex polygons in $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-04T18:05:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex polygons",
      "geometric triangulations",
      "current best lower bound",
      "planar straight-line graph",
      "maximum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1303D"
    }
  }
}