{
  "id": "2311.03868",
  "version": "v1",
  "published": "2023-11-07T10:34:29.000Z",
  "updated": "2023-11-07T10:34:29.000Z",
  "title": "The matroid of a graphing",
  "authors": [
    "László Lovász"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Graphings serve as limit objects for bounded-degree graphs. We define the ``cycle matroid'' of a graphing as a submodular setfunction, with values in [0,1], which generalizes (up to normalization) the cycle matroid of finite graphs. We prove that for a Benjamini--Schramm convergent sequence of graphs, the total rank, normalized by the number of nodes, converges to the total rank of the limit graphing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-07T10:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63",
      "05B35"
    ],
    "keywords": [
      "cycle matroid",
      "total rank",
      "benjamini-schramm convergent sequence",
      "graphings serve",
      "limit objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}