{
  "id": "2109.02633",
  "version": "v1",
  "published": "2021-09-06T17:57:27.000Z",
  "updated": "2021-09-06T17:57:27.000Z",
  "title": "Ramsey numbers of trails and circuits",
  "authors": [
    "David Conlon",
    "Mykhaylo Tyomkyn"
  ],
  "comment": "2 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that every two-colouring of the edges of the complete graph $K_n$ contains a monochromatic trail or circuit of length at least $2n^2/9 +o(n^2)$, which is asymptotically best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-06T17:57:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey numbers",
      "complete graph",
      "monochromatic trail"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}