{
  "id": "math/0606632",
  "version": "v1",
  "published": "2006-06-25T02:03:18.000Z",
  "updated": "2006-06-25T02:03:18.000Z",
  "title": "New upper bounds on the chromatic number of a graph",
  "authors": [
    "landon rabern"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We outline some ongoing work related to a conjecture of Reed \\cite{reed97} on $\\omega$, $\\Delta$, and $\\chi$. We conjecture that the complement of a counterexample $G$ to Reed's conjecture has connectivity on the order of $\\log(|G|)$. We prove that this holds for a family (parameterized by $\\epsilon > 0$) of relaxed bounds; the $\\epsilon = 0$ limit of which is Reed's upper bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-25T02:03:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C40",
      "05C69"
    ],
    "keywords": [
      "chromatic number",
      "reeds upper bound",
      "reeds conjecture",
      "ongoing work",
      "relaxed bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6632R"
    }
  }
}