{
  "abstract": "Let $\\operatorname{odd}(G)$ be the number of odd-degree vertices of a graph $G$. We prove that, if $p=o(1)$ and $np/\\log n\\to\\infty$, then with probability tending to one the random graph $G(n,p)$ has an edge decomposition into exactly $\\operatorname{odd}(G)/2$ paths. This confirms a conjecture of Glock, Kühn and Osthus from 2016. The proof combines a key lemma with cycle decompositions of random graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37173",
  "author_total": 2,
  "authors": [
    {
      "name": "Jifu Lin"
    },
    {
      "name": "Heng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9b6wj9g2hdv5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37173",
  "fulltext_url": null,
  "id": "9b6wj9g2hdv5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37173",
  "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": "W7224088616",
  "pdf_url": "https://arxiv.org/pdf/2610.37173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9b6wj9g2hdv5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Optimal path decompositions of sparse random graphs",
  "title_text": "Optimal path decompositions of sparse random graphs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9b6wj9g2hdv5d",
  "venue": "arXiv",
  "versions": []
}