{
  "abstract": "We study new higher-dimensional analogs of graph chordality and review the existing ones. Our main results for simplicial complexes are: (1) $Δ$ skeleton-E-chordal $\\Rightarrow$ $Δ^\\vee$ vertex-decomposable $\\Rightarrow$ $Δ$ skeleton-clique-chordal. Moreover, for subflag complexes, $Δ$ skeleton-E-chordal $\\Longleftrightarrow$ $Δ^\\vee$ vertex-decomposable. (For $d=1$ this boils down to ``$G$ chordal $\\Longleftrightarrow$ $G^\\vee$ vertex-decomposable'', a result closely related to Fröberg's theorem.) (2) For subflag complexes, $Δ$ is skeleton-E-chordal $\\Longleftrightarrow$ it splits as $Δ= Δ_1 \\cup Δ_2$, with each $Δ_i$ a skeleton-E-chordal induced subcomplex of $Δ$, and with $Δ_1 \\cap Δ_2$ a complex whose $1$-skeleton is a clique. (This generalizes ``$G$ chordal $\\Longleftrightarrow$ $G$ splits as a union of chordal graphs that intersect in a common clique''). (3) $Δ$ skeleton-E-chordal $\\Longleftrightarrow$ every nonempty induced subcomplex of $Δ$ has a skeleton-E-simplicial vertex. (Generalizes ``$G$ chordal $\\Leftrightarrow$ every nonempty induced subgraph has a simplicial vertex''.) (4) $Δ$ underclosed $\\Rightarrow$ $Δ$ skeleton-weakly-chordal and weakly-closed. (Generalizes ``$G$ interval $\\Rightarrow$ $G$ chordal and co-comparability''.) (5) All pure E-chordal complexes are vertex-chordal; all pure mid-chordal complexes are weakly-vertex-chordal; all pure very-weakly-chordal complexes are weakly-ridge-chordal. (This expands Bigdeli, Yazdan-Pour and Zaare-Nahandi's work on ridge-chordality.)",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21166",
  "author_total": 2,
  "authors": [
    {
      "name": "Bruno Benedetti"
    },
    {
      "name": "Marta Pavelka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87p5kk7s9x565.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21166",
  "fulltext_url": null,
  "id": "87p5kk7s9x565",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21166",
  "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.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7170635604",
  "pdf_url": "https://arxiv.org/pdf/2607.21166",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87p5kk7s9x565.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2607.21166",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21166"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Skeleton Chordalities",
  "title_text": "Skeleton Chordalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/87p5kk7s9x565",
  "venue": "arXiv",
  "versions": []
}