{
  "abstract": "We study the local $\\mathrm v$-numbers of binomial edge ideals from a combinatorial perspective. For each minimal prime $P_{\\mathcal S}$ of $J_G$, indexed by a cutset $\\mathcal S$ of $G$, we consider two combinatorial invariants, $\\mathrm v^-_{\\mathcal S}(G)$ and $\\mathrm v^+_{\\mathcal S}(G)$, defined in terms of transversals of suitable hypergraphs, and show that the local $\\mathrm v$-number $\\mathrm v_{P_{\\mathcal S}}(J_G)$ satisfies $\\mathrm v^-_{\\mathcal S}(G)\\leq \\mathrm v_{P_{\\mathcal S}}(J_G)\\leq \\mathrm v^+_{\\mathcal S}(G)$. Under a suitable hypothesis on the connected components, we provide explicit graph-theoretic descriptions of these invariants and analyze when they coincide, giving a combinatorial way to determine the local $\\mathrm v$-numbers. As an application, we derive a sufficient condition for this coincidence, which applies to a broad class of graphs. Furthermore, we identify a constant that controls the gap between $\\mathrm v^-_{\\mathcal S}(G)$ and $\\mathrm v^+_{\\mathcal S}(G)$, thereby showing that the local $\\mathrm{v}$-number lies within a bounded interval. Applications to cycles and trees illustrate both the equality criterion and the resulting bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18213",
  "author_total": 1,
  "authors": [
    {
      "name": "Emiliano Liwski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5x81qx515pkfp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18213",
  "fulltext_url": null,
  "id": "5x81qx515pkfp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18213",
  "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": "W7221834662",
  "pdf_url": "https://arxiv.org/pdf/2610.18213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5x81qx515pkfp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.18213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Combinatorial bounds for the v-number of binomial edge ideals",
  "title_text": "Combinatorial bounds for the v-number of binomial edge ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/5x81qx515pkfp",
  "venue": "arXiv",
  "versions": []
}