{
  "id": "1706.06265",
  "version": "v1",
  "published": "2017-06-20T04:47:00.000Z",
  "updated": "2017-06-20T04:47:00.000Z",
  "title": "On excluded minors for classes of graphical matroids",
  "authors": [
    "Daryl Funk",
    "Dillon Mayhew"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Frame matroids and lifted-graphic matroids are two distinct minor-closed classes of matroids, each of which generalises the class of graphic matroids. The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, simultaneously generalises both the classes of frame and lifted-graphic matroids. Let $\\mathcal{M}$ be one of these three classes, and let $r$ be a positive integer. We show that $\\mathcal{M}$ has only a finite number of excluded minors of rank $r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-20T04:47:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "excluded minors",
      "graphical matroids",
      "lifted-graphic matroids",
      "distinct minor-closed classes",
      "frame matroids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}