{
  "abstract": "In the 1960s, Erdős and Gallai conjectured that the edges of every $n$-vertex graph can be decomposed into $O(n)$ cycles and edges. We prove this conjecture. Equivalently, every Eulerian graph on $n$ vertices can be decomposed into $O(n)$ cycles, which confirms Hajós' conjecture up to a constant factor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07840",
  "author_total": 1,
  "authors": [
    {
      "name": "Jaehoon Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9t5ccyaq1an2a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07840",
  "fulltext_url": null,
  "id": "9t5ccyaq1an2a",
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  "landing_url": "https://arxiv.org/abs/2610.07840",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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      "openalex",
      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7221055617",
  "pdf_url": "https://arxiv.org/pdf/2610.07840",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9t5ccyaq1an2a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.07840",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07840"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A proof of the Erdős-Gallai cycle decomposition conjecture",
  "title_text": "A proof of the Erdős-Gallai cycle decomposition conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9t5ccyaq1an2a",
  "venue": "arXiv",
  "versions": []
}