{
  "id": "math/0408173",
  "version": "v2",
  "published": "2004-08-12T22:07:31.000Z",
  "updated": "2004-09-22T13:48:55.000Z",
  "title": "Limits of dense graph sequences",
  "authors": [
    "Laszlo Lovasz",
    "Balazs Szegedy"
  ],
  "comment": "27 pages; added extension of result (Sept 22, 2004)",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that if a sequence of dense graphs has the property that for every fixed graph F, the density of copies of F in these graphs tends to a limit, then there is a natural ``limit object'', namely a symmetric measurable 2-variable function on [0,1]. This limit object determines all the limits of subgraph densities. We also show that the graph parameters obtained as limits of subgraph densities can be characterized by ``reflection positivity'', semidefiniteness of an associated matrix. Conversely, every such function arises as a limit object. Along the lines we introduce a rather general model of random graphs, which seems to be interesting on its own right.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-09-22T13:48:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dense graph sequences",
      "subgraph densities",
      "limit object determines",
      "graphs tends",
      "random graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8173L"
    }
  }
}