{
  "id": "1411.5429",
  "version": "v1",
  "published": "2014-11-20T03:20:39.000Z",
  "updated": "2014-11-20T03:20:39.000Z",
  "title": "Permutation sorting and a game on graphs",
  "authors": [
    "C. L. Jansen",
    "M. Scheepers",
    "S. L. Simon",
    "E. Tatum"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we solve the decision problem for a specific class of finite graphs. This result is then applied to a permutation sorting game to prove the optimality of a proportional bound under which TWO has a winning strategy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-20T03:20:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05C57",
      "91A43",
      "91A46",
      "05C85",
      "05C90"
    ],
    "keywords": [
      "finite graph",
      "winning strategy",
      "general decision problem",
      "permutation sorting game",
      "specific class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.5429J"
    }
  }
}