{
  "id": "1606.00762",
  "version": "v1",
  "published": "2016-06-02T16:55:19.000Z",
  "updated": "2016-06-02T16:55:19.000Z",
  "title": "Multicolour Ramsey numbers of paths and even cycles",
  "authors": [
    "Ewan Davies",
    "Matthew Jenssen",
    "Barnaby Roberts"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that $(k-1)n+o(n)\\leq R_k(P_n)\\leq R_k(C_n)\\leq kn+o(n)$. The upper bound was recently improved by S\\'ark\\\"ozy who showed that $R_k(C_n)\\leq\\left(k-\\frac{k}{16k^3+1}\\right)n+o(n)$. Here we show $R_k(C_n) \\leq (k-\\frac14)n +o(n)$, obtaining the first improvement to the coefficient of the linear term by an absolute constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-02T16:55:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55",
      "05C38"
    ],
    "keywords": [
      "multicolour ramsey numbers",
      "upper bound",
      "absolute constant",
      "first improvement",
      "linear term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}