{
  "abstract": "A graph is said to be $H$-free if it contains no subgraph isomorphic to $H$. The generalized Turán number $\\mathrm{ex}(G, H)$, a natural extension of the classical Turán number, is defined as the maximum number of edges in an $H$-free spanning subgraph of $G$. For any integer $\\ell\\geq 2$, let $C_{2\\ell}$ denote the even cycle of length $2\\ell$. So far, extensive studies of the generalized Turán number for the hypercube $Q_{n}$ have been conducted. The $k$-ary $n$-cube is an important family of graphs with many favorable properties, such as regularity and vertex-transitivity. It generalizes the hypercube and reduces to the hypercube when $k=2$. In this paper, we investigate the generalized Turán number $\\mathrm{ex}(Q^{k}_{n}, C_{2\\ell})$ of $Q^{k}_{n}$ for all even integers $k\\geq 4$ and integers $\\ell\\geq 2$, generalizing the result for $Q_{n}$ [J. Graph Theory 16 (1992) 273-286] from $k=2$ to $k\\geq 4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05433",
  "author_total": 2,
  "authors": [
    {
      "name": "Shu-Li Zhao"
    },
    {
      "name": "Yu-Qi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/73cwz03ach9rt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05433",
  "fulltext_url": null,
  "id": "73cwz03ach9rt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05433",
  "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/2611.05433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/73cwz03ach9rt.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05433"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Extremal even-cycle-free subgraphs of the $k$-ary $n$-cube",
  "title_text": "Extremal even-cycle-free subgraphs of the k-ary n-cube",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/73cwz03ach9rt",
  "venue": "arXiv",
  "versions": []
}