{
  "id": "1708.02441",
  "version": "v1",
  "published": "2017-08-08T10:38:18.000Z",
  "updated": "2017-08-08T10:38:18.000Z",
  "title": "Cycle reversions and dichromatic number in tournaments",
  "authors": [
    "Paul Ellis",
    "Daniel T. Soukup"
  ],
  "comment": "23 pages, first public version. Comments are very welcome",
  "categories": [
    "math.CO",
    "math.LO"
  ],
  "abstract": "We show that if $D$ is a tournament of arbitrary size then $D$ has finite strong components after reversing a locally finite sequence of cycles. In turn, we prove that any tournament can be covered by two acyclic sets after reversing a locally finite sequence of cycles. This provides a partial solution to a conjecture of S. Thomass\\'e.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-08T10:38:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C63",
      "05C15",
      "05C38",
      "03E05"
    ],
    "keywords": [
      "dichromatic number",
      "cycle reversions",
      "tournament",
      "locally finite sequence",
      "finite strong components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}