{
  "id": "math/0305415",
  "version": "v1",
  "published": "2003-05-29T05:52:38.000Z",
  "updated": "2003-05-29T05:52:38.000Z",
  "title": "Kauffman-Harary conjecture holds for Montesinos Knots",
  "authors": [
    "Marta M. Asaeda",
    "Jozef H. Przytycki",
    "Adam S. Sikora"
  ],
  "comment": "to appear in Journal of Knot Theory and Ramifications, 11 pages, 10 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The Kauffman-Harary conjecture states that for any reduced alternating diagram K of a knot with a prime determinant p, every non-trivial Fox p-coloring of K assigns different colors to its arcs. We generalize the conjecture by stating it in terms of homology of the double cover of S^3 branched along a link. In this way we extend the scope of the conjecture to all prime alternating links of arbitrary determinants. We first prove the Kauffman-Harary conjecture for pretzel knots and then we generalize our argument to show the generalized Kauffman-Harary conjecture for all Montesinos links. Finally, we speculate on the relation between the conjecture and Menasco's work on incompressible surfaces in exteriors of alternating links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-29T05:52:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "kauffman-harary conjecture holds",
      "montesinos knots",
      "kauffman-harary conjecture states",
      "non-trivial fox",
      "menascos work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5415A"
    }
  }
}