{
  "abstract": "Let $F$ be a fixed graph. A graph $G$ is $F$-irregular if any two distinct vertices of $G$ belong to a different number of subgraphs of $G$ isomorphic to $F$. In this paper, we settle the strong conjecture about $F$-irregular oriented graphs (Dovzhenok, Lukashenko, and Filiuta, 2026) for the case of tournaments. Specifically, we prove that for every tournament $T$ of order $n \\ge 3$, there exists an infinite family of $T$-irregular oriented graphs. Our proof is constructive. For $n \\ge 4$, it is based on the vertex cloning method, and the underlying graphs of the constructed $T$-irregular oriented graphs are inherently $K_n$-irregular.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02760",
  "author_total": 1,
  "authors": [
    {
      "name": "Tatiana Dovzhenok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fengkrnp2c58.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02760",
  "fulltext_url": null,
  "id": "7fengkrnp2c58",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02760",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02760",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fengkrnp2c58.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02760",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02760"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Every tournament $T$ of order at least 3 admits infinitely many $T$-irregular oriented graphs",
  "title_text": "Every tournament T of order at least 3 admits infinitely many T-irregular oriented graphs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/7fengkrnp2c58",
  "venue": "arXiv",
  "versions": []
}