{
  "id": "2310.12283",
  "version": "v1",
  "published": "2023-10-17T08:10:13.000Z",
  "updated": "2023-10-17T08:10:13.000Z",
  "title": "A characterization of 4-connected graphs with no $K_{3,3}+v$-minor",
  "authors": [
    "Linsong Wei",
    "Yuqi Xu",
    "Yunxia Zhang",
    "Weihua Yang"
  ],
  "comment": "25",
  "categories": [
    "math.CO"
  ],
  "abstract": "Among graphs with 13 edges, there are exactly three internally 4-connected graphs which are $Oct^{+}$, cube+e and $ K_{3,3} +v$. A complete characterization of all 4-connected graphs with no $Oct^{+}$-minor is given in [John Maharry, An excluded minor theorem for the octahedron plus an edge, Journal of Graph Theory 57(2) (2008) 124-130]. Let $K_{3,3}+v$ denote the graph obtained by adding a new vertex $v$ to $K_{3,3}$ and joining $v$ to the four vertices of a 4-cycle. In this paper, we determine all 4-connected graphs that do not contain $K_{3,3}+v$ as a minor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-17T08:10:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete characterization",
      "graph theory",
      "john maharry",
      "octahedron plus",
      "excluded minor theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}