{
  "id": "1801.06882",
  "version": "v1",
  "published": "2018-01-21T19:22:42.000Z",
  "updated": "2018-01-21T19:22:42.000Z",
  "title": "Generalized Laminar Matroids",
  "authors": [
    "Tara Fife",
    "James Oxley"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Nested matroids were introduced by Crapo in 1965 and have appeared frequently in the literature since then. A flat of a matroid $M$ is Hamiltonian if it has a spanning circuit. A matroid $M$ is nested if and only if its Hamiltonian flats form a chain under inclusion; $M$ is laminar if and only if, for every $1$-element independent set $X$, the Hamiltonian flats of $M$ containing $X$ form a chain under inclusion. We generalize these notions to define the classes of $k$-closure-laminar and $k$-laminar matroids. This paper focuses on structural properties of these classes noting that, while the second class is always minor-closed, the first is if and only if $k \\le 3$. The main results are excluded-minor characterizations for the classes of 2-laminar and 2-closure-laminar matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-21T19:22:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "generalized laminar matroids",
      "hamiltonian flats form",
      "element independent set",
      "excluded-minor characterizations",
      "paper focuses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}