{
  "abstract": "Let $C_n^m$ be the $m$-th power of the cycle on $n$ vertices, and let $\\Gnm$ be its complement, where $m\\ge1$ and $n\\ge3m+1$. We prove that every induced subcomplex of the clique complex of $C_n^m$ is homotopy equivalent either to a disjoint union of contractible complexes or to a circle, and we establish this dichotomy for a larger class of circular interval graphs. As a consequence, we obtain a closed formula for the linear strand of the Betti table of $R/I(\\Gnm)$. We also prove that $R/I(\\Gnm)$ is a Buchsbaum ring of depth $2$ and that the independence complex of $\\Gnm$ is a triangulated $m$-manifold with boundary for $m\\ge2$, namely a Möbius band or an annulus when $m=2$. For the complement $\\overline H$ of every graph $H$ in the above class, we show that $\\reg(I(\\overline H)^k)=2k+\\indm(\\overline H)-1$ for all $k\\ge2$, where $\\indm$ denotes the induced matching number. In particular, some power of $I(\\Gnm)$ has a linear resolution if and only if $n\\ge4m+1$. In this range, we further prove that the colon ideals $(I^{k+1}:M)$, where $I=I(\\Gnm)$ and $M$ is a minimal monomial generator of $I^k$, have regularity $2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31105",
  "author_total": 1,
  "authors": [
    {
      "name": "Bilal Ahmad Wani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bjv96qjt5gf8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31105",
  "fulltext_url": null,
  "id": "bjv96qjt5gf8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31105",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.31105",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bjv96qjt5gf8m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31105",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31105"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Edge ideals of complements of a class of circular interval graphs",
  "title_text": "Edge ideals of complements of a class of circular interval graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/bjv96qjt5gf8m",
  "venue": "arXiv",
  "versions": []
}