{
  "id": "2010.01797",
  "version": "v1",
  "published": "2020-10-05T05:57:08.000Z",
  "updated": "2020-10-05T05:57:08.000Z",
  "title": "Elastic elements in 3-connected matroids",
  "authors": [
    "George Drummond",
    "Zachary Gershkoff",
    "Susan Jowett",
    "Charles Semple",
    "Jagdeep Singh"
  ],
  "comment": "15 pages, 1 fugure",
  "categories": [
    "math.CO"
  ],
  "abstract": "It follows by Bixby's Lemma that if $e$ is an element of a $3$-connected matroid $M$, then either $\\mathrm{co}(M\\backslash e)$, the cosimplification of $M\\backslash e$, or $\\mathrm{si}(M/e)$, the simplification of $M/e$, is $3$-connected. A natural question to ask is whether $M$ has an element $e$ such that both $\\mathrm{co}(M\\backslash e)$ and $\\mathrm{si}(M/e)$ are $3$-connected. Calling such an element \"elastic\", in this paper we show that if $|E(M)|\\ge 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-05T05:57:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "elastic elements",
      "bixbys lemma",
      "natural question",
      "element fans"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}