{
  "id": "0901.0929",
  "version": "v2",
  "published": "2009-01-07T21:07:59.000Z",
  "updated": "2013-08-22T15:51:11.000Z",
  "title": "Finitely forcible graphons",
  "authors": [
    "Laszlo Lovasz",
    "Balazs Szegedy"
  ],
  "comment": "revised version, 40 pages",
  "journal": "Journal of Combinatorial Theory, Series B 101 (2011), 269-301",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate families of graphs and graphons (graph limits) that are defined by a finite number of prescribed subgraph densities. Our main focus is the case when the family contains only one element, i.e., a unique structure is forced by finitely many subgraph densities. Generalizing results of Turan, Erdos-Simonovits and Chung-Graham-Wilson, we construct numerous finitely forcible graphons. Most of these fall into two categories: one type has an algebraic structure and the other type has an iterated (fractal-like) structure. We also give some necessary conditions for forcibility, which imply that finitely forcible graphons are \"rare\", and exhibit simple and explicit non-forcible graphons.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-22T15:51:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C75"
    ],
    "keywords": [
      "necessary conditions",
      "finite number",
      "algebraic structure",
      "prescribed subgraph densities",
      "unique structure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0929L"
    }
  }
}