{
  "id": "2209.03408",
  "version": "v1",
  "published": "2022-09-07T18:21:59.000Z",
  "updated": "2022-09-07T18:21:59.000Z",
  "title": "Trees maximizing the number of almost-perfect matchings",
  "authors": [
    "Stijn Cambie",
    "Bradley McCoy",
    "Gunjan Sharma",
    "Stephan Wagner",
    "Corrine Yap"
  ],
  "comment": "21 pages, 8 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings missing only one or two leaves. We also determine the trees that minimize the number of maximal matchings. We apply these results to extremal problems on the weighted Hosoya index for several choices of vertex-degree-based weight function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-07T18:21:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C09",
      "05C35",
      "05C05",
      "05C09",
      "05C35",
      "05C05",
      "05C09",
      "05C35",
      "05C70"
    ],
    "keywords": [
      "trees maximizing",
      "strong almost-perfect matchings",
      "extremal trees",
      "maximal matchings",
      "extremal problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}