{
  "id": "1809.05974",
  "version": "v1",
  "published": "2018-09-16T22:52:11.000Z",
  "updated": "2018-09-16T22:52:11.000Z",
  "title": "The extremal function for $K_9^=$ minors",
  "authors": [
    "Martin Rolek"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove the extremal function for $K_9^=$ minors, where $K_9^=$ denotes the complete graph $K_9$ with two edges removed. In particular, we show that any graph with $n$ vertices and at least $6n - 20$ edges either contains a $K_9^=$ minor or is isomorphic to a graph obtained from disjoint copies of $K_8$ and $K_{2, 2, 2, 2, 2}$ by identifying cliques of size 5. We utilize computer assistance to prove one of our lemmas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-16T22:52:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extremal function",
      "complete graph",
      "disjoint copies",
      "utilize computer assistance",
      "identifying cliques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}