{
  "abstract": "We construct an explicit minimal cellular resolution for every squarefree monomial ideal generated in degree $n-2$ in the polynomial ring $S=K[x_1,\\ldots,x_n]$. Such an ideal is the complementary edge ideal $I_c(G)$ of a simple graph $G$ on $[n]$, and the resolution is supported on a labeled regular CW complex $X_G$ of dimension at most $2$. This yields closed formulas for the differentials and for the multigraded Betti numbers of $I_c(G)$ in terms of graph invariants. We then determine the $a$-invariant of $S/I_c(G)$ in terms of the vertex connectivity of $G$. Finally, when $S/I_c(G)$ is Cohen--Macaulay, we describe the canonical module and its Hilbert series, and recover the known characterizations of the Gorenstein and level cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02168",
  "author_total": 1,
  "authors": [
    {
      "name": "Somayeh Moradi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/44sqk0htjtx1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02168",
  "fulltext_url": null,
  "id": "44sqk0htjtx1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02168",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02168",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/44sqk0htjtx1q.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02168",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02168"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minimal cellular resolutions of complementary edge ideals",
  "title_text": "Minimal cellular resolutions of complementary edge ideals",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/44sqk0htjtx1q",
  "venue": "arXiv",
  "versions": []
}