{
  "id": "2106.10023",
  "version": "v1",
  "published": "2021-06-18T09:50:40.000Z",
  "updated": "2021-06-18T09:50:40.000Z",
  "title": "Spanning $F$-cycles in random graphs",
  "authors": [
    "Alberto Espuny Díaz",
    "Yury Person"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We extend a recent argument of Kahn, Narayanan and Park (Proceedings of the AMS, to appear) about the threshold for the appearance of the square of a Hamilton cycle to other spanning structures. In particular, for any spanning graph, we give a sufficient condition under which we may determine its threshold. As an application, we find the threshold for a set of cyclically ordered copies of $C_4$ that span the entire vertex set, so that any two consecutive copies overlap in exactly one edge and all overlapping edges are disjoint. This answers a question of Frieze. We also determine the threshold for edge-overlapping spanning $K_r$-cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-18T09:50:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graphs",
      "entire vertex set",
      "hamilton cycle",
      "sufficient condition",
      "consecutive copies overlap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}