{
  "id": "1706.04903",
  "version": "v1",
  "published": "2017-06-15T14:47:30.000Z",
  "updated": "2017-06-15T14:47:30.000Z",
  "title": "A remark on Hamilton cycles with few colors",
  "authors": [
    "Igor Balla",
    "Alexey Pokrovskiy",
    "Benny Sudakov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of $K_n$ with $n$ colours contains a Hamilton cycle with $\\leq O(\\log n)$ colours. They proved that there is always a Hamilton cycle with $\\leq 8\\sqrt n$ colours. In this note we improve this bound to $O(\\log^3 n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-15T14:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C45"
    ],
    "keywords": [
      "hamilton cycle",
      "colours contains",
      "proper edge colouring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}