{
  "annotation_id": "f3e41973-c27a-4efd-9b36-1ac29da1ce32",
  "date_created": "2026-02-17T05:53:07.895000Z",
  "date_modified": "2026-02-17T05:53:07.895000Z",
  "file_hash": "7d8015c6ebbecc52453971ce8c39302338345bd187a17899a1cb52ca7397c232",
  "private": false,
  "record": {
    "abstract": "Given a claw-free graph $G=(V,E)$ with maximum degree $\\Delta$,\n  we define the parameter $\\kappa\\in [0,1]$ as $\\kappa={\\max_{v\\in V}|I_v|\\over \\lfloor\\Delta^2/4\\rfloor}$ where $I_v$ is the set of all independent pairs in the neighborhood of $v$. We refer to $\\kappa$ as the pair independence ratio of $G$.\n  We prove that for any claw-free graph $G$ with pair independence ratio at most $\\kappa$ the zeros of its chromatic polynomial $P_G(q)$ lie inside the disk $D=\\{q\\in \\mathbb{C}:~|q|\u003c C_\\kappa^0\\Delta\\}$, where $C_\\kappa^0$ is an increasing function of $\\kappa\\in [0,1]$. If $G$ is also square-free and diamond free, the function $C_\\kappa^0$ can be replaced by a sharper function $C_\\kappa^1$. These bounds constitute an improvement upon results\n  recently given by Bencs and Regts in \u0027\u0027Improved bounds on the zeros of the chromatic polynomial of graphs and claw-free graphs\u0027\u0027.",
    "arxiv_id": "2601.06918",
    "authors": [
      "Paula M. S. Fialho",
      "Aldo Procacci"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the zero-free region for the chromatic polynomial of claw-free graphs with and without induced square and induced diamond",
    "url": "https://arxiv.org/abs/2601.06918",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "45f1610c-eddb-4fd4-af4e-d836c80759b7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}