{
  "id": "math/0009230",
  "version": "v1",
  "published": "2000-09-26T22:09:53.000Z",
  "updated": "2000-09-26T22:09:53.000Z",
  "title": "The conjecture cr(C_m\\times C_n)=(m-2)n is true for all but finitely many n, for each m",
  "authors": [
    "Lev Glebsky",
    "Gelasio Salazar"
  ],
  "comment": "16 pages, plainTeX, to be subnitted to \"J. of Graph Theory\"",
  "categories": [
    "math.CO"
  ],
  "abstract": "It has been long congectured that the crossing number of $C_m\\times C_n$ is $(m-2)n$ for $2<m<=n$. In this paper we proved that conjecture is true for all but finitely many $n$ for each $m$. More specifically we proved conjecture for $n>=(m/2)((m+3)^2/2+1)$.The proof is largely based on the theory of arrangements introduced by Adamsson and further developed by Adamsson and Richter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-09-26T22:09:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C62",
      "57M15"
    ],
    "keywords": [
      "conjecture",
      "crossing number",
      "arrangements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9230G"
    }
  }
}