{
  "id": "2309.05297",
  "version": "v1",
  "published": "2023-09-11T08:29:17.000Z",
  "updated": "2023-09-11T08:29:17.000Z",
  "title": "On Ahn-Hendrey-Kim-Oum question for twin-width of graphs with 6 vertices",
  "authors": [
    "Kajal Das"
  ],
  "comment": "Comments welcome! arXiv admin note: substantial text overlap with arXiv:2207.14333",
  "categories": [
    "math.CO"
  ],
  "abstract": "Twin-width is a recently introduced graph parameter for finite graphs. It is an open problem to determine whether there is an $n$-vertex graph having twin-width at least $n/2$ (due to J. Ahn, K. Hendrey, D. Kim and S. Oum). In an earlier paper, the author showed that such a graph with less than equal to 5 vertices does not exist. In this article, we show that such a graph with 6 vertices does not exist. More precisely, we prove that each graph with 6 vertices has twin-width less than equal to 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-11T08:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05C38",
      "05C76",
      "68R10"
    ],
    "keywords": [
      "ahn-hendrey-kim-oum question",
      "twin-width",
      "graph parameter",
      "finite graphs",
      "vertex graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}