{
  "id": "2501.13670",
  "version": "v1",
  "published": "2025-01-23T13:56:11.000Z",
  "updated": "2025-01-23T13:56:11.000Z",
  "title": "Reconstruction of caterpillar tanglegrams",
  "authors": [
    "Ann Clifton",
    "Eva Czabarka",
    "Kevin Liu",
    "Sarah Loeb",
    "Utku Okur",
    "Laszlo Szekely",
    "Kristina Wicke"
  ],
  "comment": "13 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A tanglegram consists of two rooted binary trees with the same number of leaves and a perfect matching between the leaves of the trees. Given a size-$n$ tanglegram, i.e., a tanglegram for two trees with $n$ leaves, a multiset of induced size-$(n-1)$ tanglegrams is obtained by deleting a pair of matched leaves in every possible way. Here, we analyze whether a size-$n$ tanglegram is uniquely encoded by this multiset of size-$(n-1)$ tanglegrams. We answer this question affirmatively in the case that at least one of the two trees of the tanglegram is a caterpillar tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-23T13:56:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C10",
      "05C60"
    ],
    "keywords": [
      "caterpillar tanglegrams",
      "reconstruction",
      "rooted binary trees",
      "tanglegram consists",
      "caterpillar tree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}