{
  "abstract": "For a fixed graph F, the F-degree of a vertex v in a host graph H is the number of subgraphs of H isomorphic to F that contain v, and H is F-irregular if its F-degrees are pairwise distinct. We show that every finite connected graph F on at least three vertices admits a finite connected F-irregular host. For noncomplete F, the proof builds the host from a threshold graph with one deleted edge; when the minimum degree is at least two, a small incidence gadget with distinct weighted column sums separates the remaining exceptional vertices. The construction also yields infinitely many pairwise non-isomorphic finite connected F-irregular hosts for every noncomplete F. The complete-pattern case follows from a theorem of Chartrand, Holbert, Oellermann and Swart. A Lean 4 formalization of Theorem 1.1 is described, taking the published complete-pattern theorem as its sole custom axiom.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07745",
  "author_total": 1,
  "authors": [
    {
      "name": "James Alexander Schreib"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c7c4fkr1c5sm9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07745",
  "fulltext_url": null,
  "id": "c7c4fkr1c5sm9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07745",
  "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": "W7212082471",
  "pdf_url": "https://arxiv.org/pdf/2609.07745",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c7c4fkr1c5sm9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07745",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07745"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A construction of F-irregular graphs",
  "title_text": "A construction of F-irregular graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/c7c4fkr1c5sm9",
  "venue": "arXiv",
  "versions": []
}