{
  "abstract": "A forest in an edge-colored graph is rainbow if its edges have pairwise distinct colors. We prove that for every $\\varepsilon>0$ and all sufficiently large integers $m$, every properly edge-colored simple graph with $km$ edges, where $1\\leq k\\leq 2m$ and every color class has size at most $m$, contains at least $(1-\\varepsilon)m$ pairwise edge-disjoint rainbow forests, each with exactly $k$ edges. The range $k\\leq 2m$ is best possible: for every $k>2m$ there are such graphs containing no $k$-edge forest. Thus the conjecture of Montgomery, Pokrovskiy, and Sudakov fails beyond this range, while our theorem establishes its predicted conclusion throughout the largest possible range of $k$. The number of forests is asymptotically optimal. The proof uses an orientation dichotomy, hypergraph matching, matroid intersection, and martingale concentration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29351",
  "author_total": 1,
  "authors": [
    {
      "name": "Boyan Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07z4f0yq44r7k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29351",
  "fulltext_url": null,
  "id": "07z4f0yq44r7k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29351",
  "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": "W7214387107",
  "pdf_url": "https://arxiv.org/pdf/2609.29351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07z4f0yq44r7k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.29351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Nearly optimal packings of equally sized rainbow forests",
  "title_text": "Nearly optimal packings of equally sized rainbow forests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/07z4f0yq44r7k",
  "venue": "arXiv",
  "versions": []
}