{
  "id": "math/0102214",
  "version": "v1",
  "published": "2001-02-27T18:22:32.000Z",
  "updated": "2001-02-27T18:22:32.000Z",
  "title": "Upper Bound for the Coefficients of Chromatic polynomials",
  "authors": [
    "Shu-Chiuan Chang"
  ],
  "comment": "9 pages, Latex",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper describes an improvement in the upper bound for the magnitude of a coefficient of a term in the chromatic polynomial of a general graph. If $a_r$ is the coefficient of the $q^r$ term in the chromatic polynomial $P(G,q)$, where $q$ is the number of colors, then we find $a_r \\le {e \\choose v-r} - {e-g+2 \\choose v-r-g+2} + {e-k_g-g+2 \\choose v-r-g+2} - \\sum _{n=1}^{k_g-\\ell_g}\\sum_{m=1}^{\\ell_g-1} {e-g+1-n-m \\choose v-r-g} - \\delta_{g,3}\\sum_{n=1}^{k_g+\\ell_{g+1}^*-\\ell_g} {e-\\ell_g-g+1-n \\choose v-r-g}$, where $k_g$ is the number of circuits of length $g$ and $\\ell_g$ and $\\ell_{g+1}^*$ are certain numbers defined in the text.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-02-27T18:22:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "chromatic polynomial",
      "upper bound",
      "coefficient",
      "general graph"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......2214C"
    }
  }
}