{
  "abstract": "Let $T$ be a fixed tree on at least two vertices. We determine the Turán number and all extremal graphs for the Cartesian product of an odd cycle $C_{2m+1}$ and $T$, for every fixed integer $m\\ge1$ and all sufficiently large $n$, in terms of its decomposition family. Every extremal graph is the join of an independent set and an extremal graph for that family. The proof combines the Erdős--Sós theorem with weak stability and progressive induction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41286",
  "author_total": 5,
  "authors": [
    {
      "name": "Ya-Hong Chen"
    },
    {
      "name": "Yong Lu"
    },
    {
      "name": "Quan Sun"
    },
    {
      "name": "Qi Wu"
    },
    {
      "name": "Long-Tu Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/926sad6b6tk8e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41286",
  "fulltext_url": null,
  "id": "926sad6b6tk8e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41286",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/926sad6b6tk8e.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Turán number for the Cartesian product of an odd cycle and a tree",
  "title_text": "On the Turán number for the Cartesian product of an odd cycle and a tree",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/926sad6b6tk8e",
  "venue": "arXiv",
  "versions": []
}