{
  "abstract": "In this paper, we first construct two graphs $\\mathcal{F}(l,m,t,s)$ and $\\mathcal{G}_4(l,m,t,s)$. Then we introduce the graph $\\mathcal{F}_n(l,m,t,s)$ and the operator $E_{\\mathcal{G}_4(l,m,t,s)}$, where $\\mathcal{F}_n(l,m,t,s)$ is defined by identifying the vertex $c$ of $n$ copies of $\\mathcal{F}(l,m,t,s)$, and $E_{\\mathcal{G}_4(l,m,t,s)}$ is defined by replacing each edge of $G$ with $\\mathcal{G}_4(l,m,t,s)$, for any simple finite undirected graph $G$. By using the theory of Lorentzian polynomials, we prove that the independence polynomials of the graphs $\\mathcal{F}_n(l,m,t,s)$ and the image graphs of $E_{\\mathcal{G}_4(l,m,t,s)}$ are log-concave, respectively. As applications, our results not only make progress on the conjecture of Alavi, Malde, Schwenk and Erdős, but also generalize the results of Bendjeddou and Hardiman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37553",
  "author_total": 2,
  "authors": [
    {
      "name": "Lily Li Liu"
    },
    {
      "name": "Hongyue Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/erh9znwzt06qm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37553",
  "fulltext_url": null,
  "id": "erh9znwzt06qm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37553",
  "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",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214936416",
  "pdf_url": "https://arxiv.org/pdf/2609.37553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/erh9znwzt06qm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Lorentzian polynomials and log-concavity of the independence polynomials of graphs",
  "title_text": "Lorentzian polynomials and log-concavity of the independence polynomials of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/erh9znwzt06qm",
  "venue": "arXiv",
  "versions": []
}