{
  "abstract": "We prove the 3-Decomposition Conjecture: every finite connected cubic loopless multigraph decomposes into a spanning tree, a 2-regular subgraph, and a matching. The proof rests on a new theorem on matching complements in subcubic graphs. Let H be a finite connected bridgeless simple graph of maximum degree three, and let S be its set of degree-two vertices, with |S| = k >= 2. We show that H has a matching of size equal to its cyclomatic number, |E(H)| - |V(H)| + 1, whose deletion leaves a single tree containing all of S, together with cycles disjoint from S. The proof is by induction on k.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25385",
  "author_total": 1,
  "authors": [
    {
      "name": "Jicheng Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6x6fpsrdm3xzb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25385",
  "fulltext_url": null,
  "id": "6x6fpsrdm3xzb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25385",
  "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": "W7204479740",
  "pdf_url": "https://arxiv.org/pdf/2608.25385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6x6fpsrdm3xzb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2608.25385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25385"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A proof of the 3-Decomposition Conjecture",
  "title_text": "A proof of the 3-Decomposition Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/6x6fpsrdm3xzb",
  "venue": "arXiv",
  "versions": []
}