{
  "id": "2101.05264",
  "version": "v1",
  "published": "2021-01-13T18:53:35.000Z",
  "updated": "2021-01-13T18:53:35.000Z",
  "title": "Hamiltonicity in infinite tournaments",
  "authors": [
    "Ruben Melcher"
  ],
  "comment": "13 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for all countable tournaments $D$ the recently discovered compactification $|D|$ by their ends and limit edges contains a topological Hamilton path: a topological arc that contains every vertex. If $D$ is strongly connected, then $|D|$ contains a topological Hamilton circle. These results extend well-known theorems about finite tournaments, which we show do not extend to the infinite in a purely combinatorial setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-13T18:53:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C63",
      "05C20",
      "05C05",
      "05C45",
      "05C38",
      "05C85",
      "68R10"
    ],
    "keywords": [
      "infinite tournaments",
      "results extend well-known theorems",
      "hamiltonicity",
      "limit edges contains",
      "topological hamilton circle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}