{
  "id": "1611.01941",
  "version": "v1",
  "published": "2016-11-07T09:08:49.000Z",
  "updated": "2016-11-07T09:08:49.000Z",
  "title": "The Beraha number $B_{10}$ is a chromatic root",
  "authors": [
    "Gordon Royle"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This note exhibits graphs whose chromatic polynomials have the Beraha number $B_{10} = (5 + \\sqrt{5})/2$ as a root. It was previously known that no other non-integer Beraha number is a chromatic root, and so these examples complete the determination of precisely which Beraha numbers can be chromatic roots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-07T09:08:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C31",
      "05C15"
    ],
    "keywords": [
      "chromatic root",
      "non-integer beraha number",
      "chromatic polynomials",
      "examples complete"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}