{
  "abstract": "We report on an exhaustive census of all 1,006,700,565 connected graphs on $11$ vertices to find the minimal examples of graphs whose independence complexes are Cohen-Macaulay but not shellable, or shellable but not vertex decomposable. In particular, there are exactly two graphs $G$ where ${\\rm Ind}(G)$ is Cohen-Macaulay but not shellable, when the characteristic is not two, and exactly six graphs where ${\\rm Ind}(G)$ is shellable but not vertex decomposable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09926",
  "author_total": 1,
  "authors": [
    {
      "name": "Adam Van Tuyl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dchspy3xb2aqx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09926",
  "fulltext_url": null,
  "id": "dchspy3xb2aqx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09926",
  "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": "W7220958060",
  "pdf_url": "https://arxiv.org/pdf/2610.09926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dchspy3xb2aqx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09926"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minimal examples of Cohen-Macaulay independence complexes that fail to be shellable or vertex decomposable",
  "title_text": "Minimal examples of Cohen-Macaulay independence complexes that fail to be shellable or vertex decomposable",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/dchspy3xb2aqx",
  "venue": "arXiv",
  "versions": []
}