{
  "id": "2007.08800",
  "version": "v1",
  "published": "2020-07-17T07:52:28.000Z",
  "updated": "2020-07-17T07:52:28.000Z",
  "title": "Turns in Hamilton cycles of rectangular grids",
  "authors": [
    "Ethan Y. Tan",
    "Guowen Zhang"
  ],
  "comment": "28 pages, 30 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a Hamilton cycle in a rectangular $m \\times n$ grid, what is the greatest number of turns that can occur? We give the exact answer in several cases and an answer up to an additive error of $2$ in all other cases. In particular, we give a new proof of the result of Beluhov for the case of a square $n \\times n$ grid. Our main method is a surprising link between the problem of 'greatest number of turns' and the problem of 'least number of turns'.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-17T07:52:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45"
    ],
    "keywords": [
      "hamilton cycle",
      "rectangular grids",
      "greatest number",
      "main method",
      "exact answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}