{
  "abstract": "Given two tournaments of order $n$, Bollobás and Scott defined their discrepancy as the largest deviation of their overlap from its random average under relabelling, and they asked whether the resulting discrepancy is always $Ω(n^{3/2})$. We answer this question by proving that there is an absolute constant $c>0$ such that every pair of tournaments $T,U$ of order $n$ has discrepancy at least $cn^{3/2}$. More generally, if $D$ and $H$ are oriented graphs of order \\( n \\) with \\( e(D) = p \\binom{n}{2} \\) and \\( e(H) = q \\binom{n}{2} \\) satisfying $16/n \\leq p, q \\leq 1 - 16/n$, then there is an absolute constant \\( c > 0 \\) such that their discrepancy is at least $c(p(1-p)q(1-q))^{3}n^{3/2}$. We also show that these two-graph estimates extend to intersections of any fixed number of graphs, tournaments, and oriented graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27965",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhanping Yang"
    },
    {
      "name": "Qinghou Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/063vh28qfqxj2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27965",
  "fulltext_url": null,
  "id": "063vh28qfqxj2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27965",
  "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": "W7204801987",
  "pdf_url": "https://arxiv.org/pdf/2608.27965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/063vh28qfqxj2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.27965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Intersections of Oriented Graphs and Tournaments",
  "title_text": "Intersections of Oriented Graphs and Tournaments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/063vh28qfqxj2",
  "venue": "arXiv",
  "versions": []
}