{
  "id": "1904.02212",
  "version": "v1",
  "published": "2019-04-03T19:29:17.000Z",
  "updated": "2019-04-03T19:29:17.000Z",
  "title": "Regular graphs with linearly many triangles",
  "authors": [
    "Pim van der Hoorn",
    "Gabor Lippner",
    "Elchanan Mossel"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We compute the leading asymptotics of the probability that a random d-regular graph has linearly many triangles. We also show that such graphs typically consist of many disjoint $d + 1$-cliques and an almost triangle-free part.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-03T19:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C30",
      "05C75"
    ],
    "keywords": [
      "regular graphs",
      "random d-regular graph",
      "triangle-free part",
      "graphs typically consist"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}