{
  "id": "2103.07047",
  "version": "v1",
  "published": "2021-03-12T02:41:44.000Z",
  "updated": "2021-03-12T02:41:44.000Z",
  "title": "Inducibility of 4-vertex tournaments",
  "authors": [
    "Dalton Burke",
    "Bernard Lidický",
    "Florian Pfender",
    "Michael Phillips"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We determine the inducibility of all tournaments with at most $4$ vertices together with the extremal constructions. The $4$-vertex tournament containing an oriented $C_3$ and one source vertex has a particularly interesting extremal construction. It is an unbalanced blow-up of an edge, where the sink vertex is replaced by a quasi-random tournament and the source vertex is iteratively replaced by a copy of the construction itself.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-12T02:41:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inducibility",
      "source vertex",
      "particularly interesting extremal construction",
      "sink vertex",
      "quasi-random tournament"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}