{
  "id": "1908.09971",
  "version": "v1",
  "published": "2019-08-27T01:03:55.000Z",
  "updated": "2019-08-27T01:03:55.000Z",
  "title": "A note on the connectivity of 2-polymatroid minors",
  "authors": [
    "Zachary Gershkoff",
    "James Oxley"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Brylawski and Seymour independently proved that if $M$ is a connected matroid with a connected minor $N$, and $e \\in E(M) - E(N)$, then $M \\backslash e$ or $M / e$ is connected having $N$ as a minor. This paper proves an analogous but somewhat weaker result for $2$-polymatroids. Specifically, if $M$ is a connected $2$-polymatroid with a proper connected minor $N$, then there is an element $e$ of $E(M) - E(N)$ such that $M \\backslash e$ or $M / e$ is connected having $N$ as a minor. We also consider what can be said about the uniqueness of the way in which the elements of $E(M) - E(N)$ can be removed so that connectedness is always maintained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-27T01:03:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "connectivity",
      "somewhat weaker result",
      "polymatroid",
      "proper connected minor",
      "connected matroid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}