{
  "abstract": "For a fixed digraph $F$, let $\\operatorname{ex}_2^+(n,F)$ be the maximum of $\\sum_{v\\in V(D)}d_D^+(v)^2$ over all $n$-vertex $F$-free digraphs. Ai et al. [arXiv:2606.03520, 2026] asked for which self-converse tournament $F$ one can determine $\\operatorname{ex}_2^+(n,F)$. Let $TT_r$ denote a transitive tournament on $r$ vertices and $\\text{RT}_5$ denote a regular tournament on 5 vertices. Note that both $TT_r$ and $\\text{RT}_5$ are self-converse. Iľkovič [arXiv:2609.05042, 2026] determined $\\operatorname{ex}_2^+(n,F)$ for $F=TT_4$. In this paper, we determine $\\operatorname{ex}_2^+(n,F)$ for $F$ being $TT_r$ or $\\text{RT}_5$, and the latter confirms a conjecture due to Iľkovič.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01047",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhuoran Han"
    },
    {
      "name": "Yaojun Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aceaavcar74ja.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01047",
  "fulltext_url": null,
  "id": "aceaavcar74ja",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01047",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7216329981",
  "pdf_url": "https://arxiv.org/pdf/2610.01047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aceaavcar74ja.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Degree-square Turán problem for two self-converse tournaments",
  "title_text": "Degree-square Turán problem for two self-converse tournaments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/aceaavcar74ja",
  "venue": "arXiv",
  "versions": []
}