{
  "abstract": "Let $G$ be a finite simple graph and let $A_c(G)$ be the Artinian algebra associated with its cover ideal. We prove that $A_c(G)$ has the WLP when $τ(G)>|V(G)|/2$, where $τ(G)$ denotes the size of a minimum vertex cover of $G$. As a consequence, $A_c(G)$ has the WLP with high probability when the Erdős-Rényi random graph model is considered. Moreover, we study the borderline case $τ(G)=|V(G)|/2$ and as a result, classify the WLP for paths, cycles, Ferrers graphs, and well-covered trees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36674",
  "author_total": 3,
  "authors": [
    {
      "name": "Trung Chau"
    },
    {
      "name": "Tran Quang Hoa"
    },
    {
      "name": "Dang Thi Kieu Uyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37ha5ecg8dnet.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36674",
  "fulltext_url": null,
  "id": "37ha5ecg8dnet",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36674",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214938121",
  "pdf_url": "https://arxiv.org/pdf/2609.36674",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37ha5ecg8dnet.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36674",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36674"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs",
  "title_text": "Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/37ha5ecg8dnet",
  "venue": "arXiv",
  "versions": []
}