{
  "id": "2010.07911",
  "version": "v1",
  "published": "2020-10-15T17:43:30.000Z",
  "updated": "2020-10-15T17:43:30.000Z",
  "title": "A Note on Powers of Paths in Tournaments",
  "authors": [
    "Nemanja Draganić",
    "David Munhá Correia",
    "Benny Sudakov"
  ],
  "comment": "2 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note we show that every tournament on $n$ vertices contains the $k$-th power of a directed path of length $n/2^{6k+7}$, which improves upon the recent bound of Scott and Kor\\'{a}ndi of $n/2^{2^{3k}}$. By doing so, we get an inverse exponential dependence on $k$, which is best possible as Yuster recently showed an upper bound of $kn/{2^{k/2}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-15T17:43:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tournament",
      "inverse exponential dependence",
      "th power",
      "vertices contains",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}