{
  "id": "2002.07313",
  "version": "v1",
  "published": "2020-02-18T00:38:25.000Z",
  "updated": "2020-02-18T00:38:25.000Z",
  "title": "On the existence of Hamilton cycles with a periodic pattern in a random digraph",
  "authors": [
    "Alan Frieze",
    "Xavier Perez-Gimenez",
    "Pawel Pralat"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We consider Hamilton cycles in the random digraph $D_{n,m}$ where the orientation of edges follows a pattern other than the trivial orientation in which the edges are oriented in the same direction as we traverse the cycle. We show that if the orientation forms a periodic pattern, other than the trivial pattern, then approximately half the usual $n\\log n$ edges are needed to guarantee the existence of such Hamilton cycles a.a.s.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-18T00:38:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton cycles",
      "random digraph",
      "periodic pattern",
      "trivial orientation",
      "orientation forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}