{
  "id": "1312.5401",
  "version": "v2",
  "published": "2013-12-19T04:12:53.000Z",
  "updated": "2015-04-30T02:45:04.000Z",
  "title": "Fan-extensions in fragile matroids",
  "authors": [
    "Carolyn Chun",
    "Deborah Chun",
    "Dillon Mayhew",
    "Stefan H. M. van Zwam"
  ],
  "comment": "Small revisions and corrections",
  "categories": [
    "math.CO"
  ],
  "abstract": "If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when F is a minor-closed class of S-fragile matroids, and N is in F, the only members of F that contain N as a minor are obtained from N by increasing the length of fans. We prove that if this is the case, then we can certify it with a finite case-analysis. The analysis involves examining matroids that are at most two elements larger than N.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-19T04:12:53.000Z",
      "comment": "56 pages, 5 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-30T02:45:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "fan-extensions",
      "minor isomorphic",
      "elements larger",
      "excluded-minor characterizations",
      "finite case-analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.5401C"
    }
  }
}