{
  "id": "1205.4060",
  "version": "v2",
  "published": "2012-05-17T23:23:14.000Z",
  "updated": "2013-04-22T12:00:01.000Z",
  "title": "Dense flag triangulations of 3-manifolds via extremal graph theory",
  "authors": [
    "Michal Adamaszek",
    "Jan Hladky"
  ],
  "comment": "Trans. AMS, to appear",
  "categories": [
    "math.CO"
  ],
  "abstract": "We characterize f-vectors of sufficiently large three-dimensional flag Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete Comput. Geom., 34 (2), 269--284, 2005]. In particular, this characterizes f-vectors of large flag triangulations of the 3-sphere. Actually, our main result is more general and describes the structure of closed flag 3-manifolds which have many edges. Looking at the 1-skeleta of these manifolds we reduce the problem to a certain question in extremal graph theory. We then resolve this question by employing the Supersaturation Theorem of Erdos and Simonovits.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-22T12:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extremal graph theory",
      "dense flag triangulations",
      "sufficiently large three-dimensional flag",
      "large flag triangulations",
      "characterizes f-vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.4060A"
    }
  }
}