{
  "id": "1510.00417",
  "version": "v1",
  "published": "2015-10-01T20:32:10.000Z",
  "updated": "2015-10-01T20:32:10.000Z",
  "title": "A zero-free interval for chromatic polynomials of graphs with 3-leaf spanning trees",
  "authors": [
    "Thomas Perrett"
  ],
  "comment": "16 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is proved that if $G$ is a graph containing a spanning tree with at most three leaves, then the chromatic polynomial of $G$ has no roots in the interval $(1,t_1]$, where $t_1 \\approx 1.2904$ is the smallest real root of the polynomial $(t-2)^6 +4(t-1)^2(t-2)^3 -(t-1)^4$. We also construct a family of graphs containing such spanning trees with chromatic roots converging to $t_1$ from above. We employ the Whitney $2$-switch operation to manage the analysis of an infinite class of chromatic polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T20:32:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C31"
    ],
    "keywords": [
      "chromatic polynomial",
      "spanning tree",
      "zero-free interval",
      "smallest real root",
      "infinite class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000417P"
    }
  }
}