{
  "id": "1601.07149",
  "version": "v1",
  "published": "2016-01-26T20:14:37.000Z",
  "updated": "2016-01-26T20:14:37.000Z",
  "title": "Inducibility in binary trees and crossings in random tanglegrams",
  "authors": [
    "Éva Czabarka",
    "László A. Székely",
    "Stephan Wagner"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $\\gamma(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that induce a tree isomorphic to $B$. The inducibility of $B$ is $\\limsup_{|T| \\to \\infty} \\gamma(B,T)$. We determine the inducibility in some special cases, show that every binary tree has positive inducibility and prove that caterpillars are the only binary trees with inducibility $1$. We also formulate some open problems and conjectures on the inducibility. Finally, we present an application to crossing numbers of random tanglegrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-26T20:14:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inducibility",
      "random tanglegrams",
      "fixed rooted binary tree",
      "similar nature",
      "tree isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}