{
  "abstract": "For a simple graph $G$ with $n$ vertices, its $w$-polynomial is defined by \\begin{align*} \\sum_{q\\geq0}P(G;q)x^q =\\frac{w(G;x)}{(1-x)^{n+1}}, \\end{align*} where $P(G;x)$ is the chromatic polynomial of $G$. This polynomial was introduced by Brenti in 1992. In this paper, we prove Conjecture~6.7 and the $w$-assertion of Conjecture~6.5 posed by Brenti, Royle and Wagner in 1994. The first states that $w(C_n;x)$ has only real zeros for $n\\ge 5$. The second assertion states that if $G\\cap H$ is complete and both $w(G;x)$ and $w(H;x)$ have only real zeros, then $w(G\\cup H;x)$ has only real zeros.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00912",
  "author_total": 2,
  "authors": [
    {
      "name": "Hongyue Tang"
    },
    {
      "name": "Lily Li Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/33saj10s21jxz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00912",
  "fulltext_url": null,
  "id": "33saj10s21jxz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00912",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/33saj10s21jxz.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Real zeros of $w$-polynomials: cycles and complete cutsets",
  "title_text": "Real zeros of w-polynomials: cycles and complete cutsets",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/33saj10s21jxz",
  "venue": "arXiv",
  "versions": []
}