{
  "id": "1405.6808",
  "version": "v1",
  "published": "2014-05-27T06:40:10.000Z",
  "updated": "2014-05-27T06:40:10.000Z",
  "title": "More on quasi-random graphs, subgraph counts and graph limits",
  "authors": [
    "Svante Janson",
    "Vera T. Sós"
  ],
  "comment": "35 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It has been shown by several authors that several such conditions are quasi-random, but that there are exceptions. In order to understand this better, we investigate some new properties of this type. We show that these properties too are quasi-random, at least in some cases; however, there are also cases that are left as open problems, and we discuss why the proofs fail in these cases. The proofs are based on the theory of graph limits; and on the method and results developed by Janson (2011), this translates the combinatorial problem to an analytic problem, which then is translated to an algebraic problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-27T06:40:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C99"
    ],
    "keywords": [
      "graph limits",
      "quasi-random graphs",
      "subgraph counts",
      "properties",
      "analytic problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6808J"
    }
  }
}