{
  "abstract": "An oriented graph $H$ is said to be tournament anti-Sidorenko (TAS) if a uniformly random tournament asymptotically maximizes the homomorphism density of $H$ among all tournaments. For an oriented path $P$, a direction flip is a non-leaf source or sink. Sah, Sawhney and Zhao proved that consistently directed paths (paths with no direction flips) are TAS. He, Mani, Nie, Tung and Wei proved that for $3\\le k\\le 7$, every oriented path of length $k$ with exactly one direction flip is TAS, and Chen, Clemen and Noel recently extended this to every $k\\ge 3$. In this paper, we extend these results by proving that for every integer $r\\ge 0$, every oriented path of length at least $1665r+1454$ with $r$ direction flips is tournament anti-Sidorenko.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14655",
  "author_total": 2,
  "authors": [
    {
      "name": "Hao Chen"
    },
    {
      "name": "Yupeng Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8vv01jsqqy2m5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14655",
  "fulltext_url": null,
  "id": "8vv01jsqqy2m5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14655",
  "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": "W7213277102",
  "pdf_url": "https://arxiv.org/pdf/2609.14655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8vv01jsqqy2m5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14655"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko",
  "title_text": "Oriented Paths with Few Direction Flips Are Tournament Anti-Sidorenko",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/8vv01jsqqy2m5",
  "venue": "arXiv",
  "versions": []
}