{
  "id": "2102.02010",
  "version": "v1",
  "published": "2021-02-03T11:25:00.000Z",
  "updated": "2021-02-03T11:25:00.000Z",
  "title": "Inducibility and universality for trees",
  "authors": [
    "Timothy F. N. Chan",
    "Daniel Kral",
    "Bojan Mohar",
    "David R. Wood"
  ],
  "comment": "31 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive $\\varepsilon_1$ and $\\varepsilon_2$ such that every tree that is neither a path nor a star has inducibility at most $1-\\varepsilon_1$, where the inducibility of a tree $T$ is defined as the maximum limit density of $T$, and that there are infinitely many trees with inducibility at least $\\varepsilon_2$. Finally, we construct a universal sequence of trees; that is, a sequence in which the limit density of any tree is positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T11:25:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inducibility",
      "universality",
      "maximum limit density",
      "universal sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}