{
  "abstract": "Bourneuf, Charbit and Thomassé [BCT25] showed that the domination number of a tournament can be bounded as a function of its fractional dichromatic number. The function proved was exponential and the tools were based on VC-dimension. In this paper, we present two new proofs of this theorem. The first proof is based on a reduction to the problem of bounding the domination number of a $(1/2-ε)$-majority tournament, for which [BCT25] and Charikar, Ramakrishnan and Wang [CRW26] gave tight bounds. This proof yields the same exponential bound on the domination number as in [BCT25]. The second proof gives a quasilinear bound for the domination in terms of the fractional dichromatic number. It was obtained via AI and was inspired by the recent book proof of the existence of a Condorcet Winning Set of size five due to Ramakrishnan [Ram26].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35186",
  "author_total": 2,
  "authors": [
    {
      "name": "Paul Colinot"
    },
    {
      "name": "Alantha Newman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jdnwyn0q04e6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35186",
  "fulltext_url": null,
  "id": "4jdnwyn0q04e6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35186",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214725924",
  "pdf_url": "https://arxiv.org/pdf/2609.35186",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jdnwyn0q04e6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35186",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35186"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Fractional Dichromatic Number and Domination in Tournaments",
  "title_text": "Fractional Dichromatic Number and Domination in Tournaments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/4jdnwyn0q04e6",
  "venue": "arXiv",
  "versions": []
}