{
  "id": "1407.7092",
  "version": "v1",
  "published": "2014-07-26T03:49:54.000Z",
  "updated": "2014-07-26T03:49:54.000Z",
  "title": "Ramsey numbers of paths and graphs of the same order",
  "authors": [
    "Chaoping Pei",
    "Yusheng Li"
  ],
  "comment": "8 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For graphs $F_n$ and $G_n$ of order $n$, if $R(F_n, G_n)=(\\chi(G_n)-1)(n-1)+\\sigma(G_n)$, then $F_n$ is said to be $G_n$-good, where $\\sigma(G_n)$ is the minimum size of a color class among all proper vertex-colorings of $G_n$ with $\\chi(G_n)$ colors. Given $\\Delta(G_n)\\le \\Delta$, it is shown that $P_n$ is asymptotically $G_n$-good if $\\alpha(G_n)\\le\\frac{n}{4}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-26T03:49:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramsey numbers",
      "color class",
      "proper vertex-colorings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7092P"
    }
  }
}