{
  "abstract": "In earlier work, we proved that the length polyhedron of an interval order has a unique Hilbert basis and that every element of this basis is a binary vector. The supports of these binary vectors form a set system whose intersection graph is a cocomparability graph. This leads naturally to the question of which graphs can arise as intersection graphs of such Hilbert-basis supports. We introduce Hilbert fragments, defined as induced subgraphs of these intersection graphs. Thus Hilbert fragments form a hereditary class of cocomparability graphs recording the intersection patterns among the supports of Hilbert-basis elements of interval-order length polyhedra. We characterize Hilbert fragments by an axiomatically defined vertex-labeling, called a track-labeling, and give applications illustrating how this characterization can reveal an underlying one-dimensional structure even when the Hilbert fragments themselves are not interval graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02450",
  "author_total": 3,
  "authors": [
    {
      "name": "Csaba Biró"
    },
    {
      "name": "André E. Kézdy"
    },
    {
      "name": "Jen\\Ho Lehel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dh3q9j5gtttjb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02450",
  "fulltext_url": null,
  "id": "dh3q9j5gtttjb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02450",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7220379792",
  "pdf_url": "https://arxiv.org/pdf/2610.02450",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dh3q9j5gtttjb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.02450",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02450"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hilbert fragments",
  "title_text": "Hilbert fragments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/dh3q9j5gtttjb",
  "venue": "arXiv",
  "versions": []
}