{
  "abstract": "We prove that there is an absolute constant $c>0$ such that every connected vertex-transitive graph $G$ on $n \\ge 3$ vertices contains a cycle of length at least $cn$. Moreover, every such graph with sufficiently large degree $d$ contains a cycle of length at least $(1-d^{-1/100})n$. This gives the first linear bound towards Lovász's Hamiltonicity conjecture. The proof combines a structural result of DeVos and Mohar on vertex-transitive graphs with a general framework for finding long cycles, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02053",
  "author_total": 2,
  "authors": [
    {
      "name": "Jie Ma"
    },
    {
      "name": "Ziyuan Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ag0sdty10dhj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02053",
  "fulltext_url": null,
  "id": "0ag0sdty10dhj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02053",
  "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": "W7215722501",
  "pdf_url": "https://arxiv.org/pdf/2610.02053",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ag0sdty10dhj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02053",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02053"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Linear circumference in vertex-transitive graphs",
  "title_text": "Linear circumference in vertex-transitive graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/0ag0sdty10dhj",
  "venue": "arXiv",
  "versions": []
}