{
  "abstract": "Let $I = I(G)$ be the edge ideal of a finite simple graph $G$. We investigate the relationship between the associated primes and $v$-numbers of powers $I^t$ and their integral closures $\\overline{I^t}$. For the third power, we establish the associated prime containment $\\operatorname{Ass}(S/\\overline{I^3}) \\subseteq \\operatorname{Ass}(S/I^3)$, which yields $v(I^3) \\le v(\\overline{I^3})$. In contrast, for $t \\ge 4$, we show that $\\operatorname{Ass}(S/\\overline{I^t})$ and $\\operatorname{Ass}(S/I^t)$ are in general incomparable. Furthermore, for every fixed $t \\ge 3$ and $r\\ge 4$, we construct families of graphs for which the discrepancies $v(\\overline{I^t}) - v(I^t)$ and $v(I^r)-v(\\overline{I^r})$ are arbitrarily large.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31901",
  "author_total": 3,
  "authors": [
    {
      "name": "Trung Chau"
    },
    {
      "name": "Tai Huy Ha"
    },
    {
      "name": "Thanh Vu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vsztbnw82wdb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31901",
  "fulltext_url": null,
  "id": "2vsztbnw82wdb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31901",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7223674513",
  "pdf_url": "https://arxiv.org/pdf/2610.31901",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vsztbnw82wdb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.31901",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31901"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Associated primes and v-numbers of integral closures of powers of edge ideals",
  "title_text": "Associated primes and v-numbers of integral closures of powers of edge ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2vsztbnw82wdb",
  "venue": "arXiv",
  "versions": []
}