{
  "id": "1411.1850",
  "version": "v1",
  "published": "2014-11-07T07:08:51.000Z",
  "updated": "2014-11-07T07:08:51.000Z",
  "title": "Stick numbers of $2$-bridge knots and links",
  "authors": [
    "Youngsik Huh",
    "Sungjong No",
    "Seungsang Oh"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "Negami found an upper bound on the stick number $s(K)$ of a nontrivial knot $K$ in terms of the minimal crossing number $c(K)$ of the knot which is $s(K) \\leq 2 c(K)$. Furthermore McCabe proved $s(K) \\leq c(K) + 3$ for a $2$-bridge knot or link, except in the case of the unlink and the Hopf link. In this paper we construct any $2$-bridge knot or link $K$ of at least six crossings by using only $c(K)+2$ straight sticks. This gives a new upper bound on stick numbers of $2$-bridge knots and links in terms of crossing numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-07T07:08:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "bridge knot",
      "stick number",
      "upper bound",
      "nontrivial knot",
      "hopf link"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1850H"
    }
  }
}