{
  "id": "1905.01830",
  "version": "v1",
  "published": "2019-05-06T06:01:58.000Z",
  "updated": "2019-05-06T06:01:58.000Z",
  "title": "Well-quasi-order of plane minors and an application to link diagrams",
  "authors": [
    "Carolina Medina",
    "Bojan Mohar",
    "Gelasio Salazar"
  ],
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "A plane graph $H$ is a {\\em plane minor} of a plane graph $G$ if there is a sequence of vertex and edge deletions, and edge contractions performed on the plane, that takes $G$ to $H$. Motivated by knot theory problems, it has been asked if the plane minor relation is a well-quasi-order. We settle this in the affirmative. We also prove an additional application to knot theory. If $L$ is a link and $D$ is a link diagram, write $D\\leadsto L$ if there is a sequence of crossing exchanges and smoothings that takes $D$ to a diagram of $L$. We show that, for each fixed link $L$, there is a polynomial-time algorithm that takes as input a link diagram $D$ and answers whether or not $D\\leadsto L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-06T06:01:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "05C83",
      "05C10",
      "57M25"
    ],
    "keywords": [
      "link diagram",
      "well-quasi-order",
      "plane graph",
      "knot theory problems",
      "plane minor relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}