{
  "id": "1701.08049",
  "version": "v1",
  "published": "2017-01-27T13:37:11.000Z",
  "updated": "2017-01-27T13:37:11.000Z",
  "title": "On a conjecture of Sokal concerning roots of the independence polynomial",
  "authors": [
    "Han Peter",
    "Guus Regts"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO",
    "cs.DS",
    "math.DS"
  ],
  "abstract": "A conjecture of Sokal (2001) regarding the domain of non-vanishing for independence polynomials of graphs, states that given any natural number $\\Delta \\ge 3$, there exists a neighborhood in $\\mathbb C$ of the interval $[0, \\frac{(\\Delta-1)^{\\Delta-1}}{(\\Delta-2)^{\\Delta}})$ on which the independence polynomial of any graph with maximum degree at most $\\Delta$ does not vanish. We show here that Sokal's Conjecture holds, as well as a multivariate version, and prove optimality for the domain of non-vanishing. An important step is to translate the setting to the language of complex dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-27T13:37:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "independence polynomial",
      "sokal concerning roots",
      "sokals conjecture holds",
      "complex dynamical systems",
      "important step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}