{
  "id": "1312.2081",
  "version": "v1",
  "published": "2013-12-07T10:11:20.000Z",
  "updated": "2013-12-07T10:11:20.000Z",
  "title": "The Ramsey numbers of paths versus wheels: a complete solution",
  "authors": [
    "Binlong Li",
    "Bo Ning"
  ],
  "comment": "32 pages, 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G_1$ and $G_2$ be two given graphs. The Ramsey number $R(G_1,G_2)$ is the least integer $r$ such that for every graph $G$ on $r$ vertices, either $G$ contains a $G_1$ or $\\overline{G}$ contains a $G_2$. We denote by $P_n$ the path on $n$ vertices and $W_m$ the wheel on $m+1$ vertices. Chen et al. and Zhang determined the values of $R(P_n,W_m)$ when $m\\leq n+1$ and when $n+2\\leq m\\leq 2n$, respectively. In this paper we determine all the values of $R(P_n,W_m)$ for the left case $m\\geq 2n+1$. Together with Chen et al's and Zhang's results, we give a complete solution to the problem of determining the Ramsey numbers of paths versus wheels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-07T10:11:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55",
      "05D10"
    ],
    "keywords": [
      "ramsey number",
      "complete solution",
      "left case",
      "zhangs results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.2081L"
    }
  }
}