{
  "abstract": "A longstanding fundamental problem of Burr, Erdős, Faudree, Rousseau and Schelp (\\emph{Trans. Amer. Math. Soc.}, 1982) is to determine the exact value of the least integer $f(m)$, for odd $m\\ge3$, such that every tree $T_n$ on $n\\ge f(m)$ vertices satisfies $R(T_n,C_m)=2n-1$. We settle this problem for all sufficiently large odd $m$. Indeed, we establish $$f(m)=\\left\\lceil \\frac{2m-1}{3} \\right\\rceil$$ for all such $m$, where the lower bound follows from a result by Faudree, Lawrence, Parsons and Schelp. This also confirms a conjecture of Huang, Zhang and Chen for all such $m$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00944",
  "author_total": 2,
  "authors": [
    {
      "name": "Qizhong Lin"
    },
    {
      "name": "Chunlin You"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kaxdsyj11b7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00944",
  "fulltext_url": null,
  "id": "2kaxdsyj11b7y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00944",
  "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": "W7206181697",
  "pdf_url": "https://arxiv.org/pdf/2609.00944",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kaxdsyj11b7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.00944",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00944"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Ramsey threshold for trees versus odd cycles",
  "title_text": "The Ramsey threshold for trees versus odd cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/2kaxdsyj11b7y",
  "venue": "arXiv",
  "versions": []
}