{
  "id": "2210.13998",
  "version": "v1",
  "published": "2022-10-25T13:11:53.000Z",
  "updated": "2022-10-25T13:11:53.000Z",
  "title": "Ramsey numbers of large even cycles and fans",
  "authors": [
    "Chunlin You",
    "Qizhong Lin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For graphs $F$ and $H$, the Ramsey number $R(F, H)$ is the smallest positive integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $F$ or a blue $H$. Let $C_n$ be a cycle of length $n$ and $F_n$ be a fan consisting of $n$ triangles all sharing a common vertex. In this paper, we prove that for all sufficiently large $n$, \\[ R(C_{2\\lfloor an\\rfloor}, F_n)= \\left\\{ \\begin{array}{ll} (2+2a+o(1))n & \\textrm{if $1/2\\leq a< 1$,}\\\\ (4a+o(1))n & \\textrm{if $ a\\geq 1$.} \\end{array} \\right. \\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-25T13:11:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey number",
      "smallest positive integer",
      "common vertex",
      "red/blue edge coloring",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}