{
  "id": "2311.01672",
  "version": "v1",
  "published": "2023-11-03T02:37:38.000Z",
  "updated": "2023-11-03T02:37:38.000Z",
  "title": "Counterexamples to Negami's Conjecture have ply at least 14",
  "authors": [
    "Dickson Y. B. Annor",
    "Yuri Nikolayevsky",
    "Michael S. Payne"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "S. Negami conjectured in $1988$ that a connected graph has a finite planar cover if and only if it embeds in the projective plane. It follows from the works of D. Archdeacon, M. Fellows, P. Hlin\\v{e}n\\'{y}, and S. Negami that the conjecture is true if the graph $K_{2, 2, 2, 1}$ has no finite planar cover. We prove that $K_{2, 2, 2, 1}$ has no planar cover of ply less than $14$ and consequently, any counterexample to Negami's conjecture has ply at least 14 and at least $98$ vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-03T02:37:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "57M15"
    ],
    "keywords": [
      "negamis conjecture",
      "finite planar cover",
      "counterexample",
      "projective plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}