{
  "id": "2007.10272",
  "version": "v1",
  "published": "2020-07-20T16:54:40.000Z",
  "updated": "2020-07-20T16:54:40.000Z",
  "title": "Merge trees in discrete Morse theory",
  "authors": [
    "Benjamin Johnson",
    "Nicholas A. Scoville"
  ],
  "categories": [
    "math.AT",
    "math.CO"
  ],
  "abstract": "In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse functions based on the induced merge tree. We then relate the matching number of a tree to a certain invariant of the induced merge tree. Finally, we count the number of merge trees that can be induced on a star graph and characterize the induced merge tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-20T16:54:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete morse theory",
      "induced merge tree",
      "discrete morse function",
      "study merge trees",
      "star graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}