{
  "abstract": "For graphs $H$ and $F$, let $\\text{ex}(n,H,F)$ denote the maximum number of copies of $H$ in an $n$-vertex $F$-free graph. Gerbner, Győri, Methuku, and Vizer proved that $\\text{ex}(n,C_{2\\ell},C_{2k})=Θ(n^\\ell)$ for $k>\\ell\\ge2$. They determined the leading term for $\\ell=2$, but for $k>\\ell\\ge3$ their general lower and upper bounds had different leading constants, leaving open the problem of closing this gap. We solve this problem by showing that, for every $k>\\ell\\ge2$, \\[\\text{ex}(n,C_{2\\ell},C_{2k})=\\left(\\frac{(k-1)_\\ell}{2\\ell}+o(1)\\right)n^\\ell, \\] where $(k-1)_\\ell=(k-1)(k-2)\\cdots(k-\\ell)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37376",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhen Liu"
    },
    {
      "name": "Chuanshu Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgtwc4b5rc294.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37376",
  "fulltext_url": null,
  "id": "bgtwc4b5rc294",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37376",
  "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": "W7214994356",
  "pdf_url": "https://arxiv.org/pdf/2609.37376",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgtwc4b5rc294.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37376",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37376"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Generalized Turán problems for shorter even cycles",
  "title_text": "Generalized Turán problems for shorter even cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/bgtwc4b5rc294",
  "venue": "arXiv",
  "versions": []
}