{
  "abstract": "A set of vertices in a digraph is majority-stable if each of its vertices has at most half of its outneighbors in the set. A fractional majority coloring assigns nonnegative weights to such sets, covering each vertex to total weight at least one; its minimum total weight is the fractional majority coloring number. We prove that every finite loopless digraph has fractional majority coloring number at most \\(523/140<3.736\\), improving the bound \\(3.9602\\) of Anastos, Lamaison, Steiner and Szabó. Our construction uses exclusive sampling from pairs in random cycle matchings, followed by deletion and a correction on the acyclic remainder. The same approach yields bounds below \\(3.430\\) for digraphs with a directed cycle factor, \\(3.287\\) for those with an even cycle factor, and \\(3.324\\) for tournaments. As a consequence, for every fixed \\(\\varepsilon>0\\), we obtain a randomized \\((2.491+\\varepsilon)\\)-approximation algorithm producing an explicit fractional majority coloring in expected polynomial time. On the complexity side, we prove NP-completeness of deciding whether the fractional majority coloring number equals $3/2$, and establish a multiplicative inapproximability threshold of $72/71$ and an additive upper-estimation threshold of $3/142$. All three results hold for acyclic oriented digraphs with outdegrees zero or two in which every directed path has length at most two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11997",
  "author_total": 2,
  "authors": [
    {
      "name": "Walid Ben-Ameur"
    },
    {
      "name": "Alessandro Maddaloni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/804x0trm2dmfd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11997",
  "fulltext_url": null,
  "id": "804x0trm2dmfd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11997",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7221152352",
  "pdf_url": "https://arxiv.org/pdf/2610.11997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/804x0trm2dmfd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Fractional majority coloring of digraphs: bounds and inapproximability",
  "title_text": "Fractional majority coloring of digraphs: bounds and inapproximability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/804x0trm2dmfd",
  "venue": "arXiv",
  "versions": []
}