{
  "id": "1907.09338",
  "version": "v1",
  "published": "2019-07-22T14:29:26.000Z",
  "updated": "2019-07-22T14:29:26.000Z",
  "title": "A Cantor-Bernstein-type theorem for spanning trees in infinite graphs",
  "authors": [
    "Joshua Erde",
    "Pascal Gollin",
    "Atilla Joó",
    "Paul Knappe",
    "Max Pitz"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that if a graph admits a packing and a covering both consisting of $\\lambda$ many spanning trees, where $\\lambda$ is some infinite cardinal, then the graph also admits a decomposition into $\\lambda$ many spanning trees. For finite $\\lambda$ the analogous question remains open, however, a slightly weaker statement is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-22T14:29:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63",
      "05C40"
    ],
    "keywords": [
      "spanning trees",
      "infinite graphs",
      "cantor-bernstein-type theorem",
      "analogous question remains open",
      "graph admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}