{
  "abstract": "An oriented graph $\\vec{H}$ is said to be tournament anti-Sidorenko if the homomorphism density of $\\vec{H}$ in any tournament $\\vec{T}$ is bounded above by the homomorphism density of $\\vec{H}$ in a large uniformly random tournament. We prove the following: (1) Every oriented path with at least three arcs and exactly one non-leaf source or sink vertex is tournament anti-Sidorenko. (2) An oriented path is tournament anti-Sidorenko if the distance between any leaf vertex and any source or sink vertex is at least two and the distance between any pair of non-leaf source or sink vertices is a multiple of four. (3) Every spider with exactly three legs admits a tournament anti-Sidorenko orientation. The first result proves a conjecture posed by He, Mani, Nie, Tung and Wei. The third resolves a problem from the same paper, in fact establishing a substantially more general statement, and provides evidence in support of a conjecture of Fox, Himwich, Mani and Zhou. The second yields the first family of tournament anti-Sidorenko oriented paths which is exponentially large with respect to the number of arcs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.14138",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao Chen"
    },
    {
      "name": "Felix Christian Clemen"
    },
    {
      "name": "Jonathan A. Noel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6zha928ffk2wr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14138",
  "fulltext_url": null,
  "id": "6zha928ffk2wr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14138",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7161268947",
  "pdf_url": "https://arxiv.org/pdf/2605.14138",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6zha928ffk2wr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2605.14138",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14138"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Tournament Anti-Sidorenko Orientations of Trees",
  "title_text": "On Tournament Anti-Sidorenko Orientations of Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/6zha928ffk2wr",
  "venue": "arXiv",
  "versions": []
}