{
  "id": "math/0609012",
  "version": "v1",
  "published": "2006-09-01T02:34:24.000Z",
  "updated": "2006-09-01T02:34:24.000Z",
  "title": "The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial",
  "authors": [
    "Sergei Chmutov",
    "Igor Pak"
  ],
  "comment": "This is a completely rewritten version of the previos preprint math.GT/0404475 oriented to topological applications to virtual links. To be published in the Moscow Mathematical Journal",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollob\\'as-Riordan polynomial $R_{G_L}$ of a ribbon graph associated with $L$. This result generalizes Thistlethwaite's celebrated theorem relating the Kauffman bracket with the Tutte polynomial of planar graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-01T02:34:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "05C10"
    ],
    "keywords": [
      "kauffman bracket",
      "bollobás-riordan polynomial",
      "thistlethwaites celebrated theorem relating",
      "result generalizes thistlethwaites celebrated theorem",
      "checkerboard colorable virtual link"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9012C"
    }
  }
}