{
  "id": "1512.03592",
  "version": "v1",
  "published": "2015-12-11T10:49:00.000Z",
  "updated": "2015-12-11T10:49:00.000Z",
  "title": "An upper bound on stick numbers of knots",
  "authors": [
    "Youngsik Huh",
    "Seungsang Oh"
  ],
  "doi": "10.1142/S0218216511008966",
  "categories": [
    "math.GT"
  ],
  "abstract": "In 1991, 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 $s(K) \\leq 2 c(K)$. In this paper we improve this upper bound to $s(K) \\leq \\frac{3}{2} (c(K)+1)$. Moreover if $K$ is a non-alternating prime knot, then $s(K) \\leq \\frac{3}{2} c(K)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-11T10:49:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "upper bound",
      "stick number",
      "minimal crossing number",
      "nontrivial knot"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}