{
  "abstract": "A graph $G$ is said to be $H$-free if it contains no copy of $H$. 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 $G$. Although $\\mathrm{ex}(G, H)$ has been extensively studied for various specific graphs $G$, such as hypercubes, complete transposition graphs, and doubled Johnson graphs, very few results are known for general graphs. For a graph $G$ of girth $g$, let $C_{g}$ denote the cycle of length $g$. In this paper, we investigate the generalized Turán number $\\mathrm{ex}(G, C_{g})$ for graphs $G$ in which every edge is contained in a fixed number of $g$-cycles, and establish a general upper bound on it. This bound generalizes the classical results on hypercubes and provides a unified approach for general graphs. Furthermore, we apply this bound to derive explicit upper bounds for several specific graphs, including $K_{n,n,\\ldots,n}$, $K_{n}\\times K_{n}$, $C_{m}\\times C_{n}$, $S_{n}$, $AG_{n}$, $CT_{n}$ and $J(n;k,k+1)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08547",
  "author_total": 2,
  "authors": [
    {
      "name": "Shu-Li Zhao"
    },
    {
      "name": "Yu-Qi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72vjmt7qx2sjj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08547",
  "fulltext_url": null,
  "id": "72vjmt7qx2sjj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08547",
  "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/2611.08547",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72vjmt7qx2sjj.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08547",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08547"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Upper bound on the size of subgraphs avoiding cycles of girth length in graphs",
  "title_text": "Upper bound on the size of subgraphs avoiding cycles of girth length in graphs",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/72vjmt7qx2sjj",
  "venue": "arXiv",
  "versions": []
}