{
  "abstract": "Let $G_n$ be the bipartite complement of the even cycle $C_{2n}$, and let $J_{G_n}$ be its binomial edge ideal. For $n\\geq5$, we study the interaction between the combinatorial structure of $G_n$ and the algebraic invariants of $S_{G_n}/J_{G_n}$. Our main combinatorial ingredient is a classification of the subsets of $V(G_n)$ having the cut point property, obtained through an analysis of disconnected induced subgraphs of $G_n$. We use this classification to describe the minimal primes and to study dimension and degree-theoretic invariants of $J_{G_n}$ and $S_{G_n}/J_{G_n}$. We also study local Vasconcelos numbers, graded Betti numbers and the Hilbert series, and obtain information on projective dimension and depth. Finally, we analyze induced paths in $G_n$ and derive corresponding bounds for the Castelnuovo--Mumford regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32860",
  "author_total": 3,
  "authors": [
    {
      "name": "Shahnawaz Ahmad Rather"
    },
    {
      "name": "S. Pirzada"
    },
    {
      "name": "M. Aijaz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6xsnb1s1yejy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32860",
  "fulltext_url": null,
  "id": "f6xsnb1s1yejy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32860",
  "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"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214738396",
  "pdf_url": "https://arxiv.org/pdf/2609.32860",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6xsnb1s1yejy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32860",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32860"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Binomial edge ideals of bipartite complements of even cycles",
  "title_text": "Binomial edge ideals of bipartite complements of even cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/f6xsnb1s1yejy",
  "venue": "arXiv",
  "versions": []
}