{
  "abstract": "A Berge path in a hypergraph is an alternating sequence of distinct vertices and edges $v_1,e_1, v_2, \\ldots, e_{k-1}, v_{k}$ such that $v_i, v_{i+1} \\in e_i$ for all $i \\in [k-1]$. Győri, Katona, and Lemons determined the maximum number of edges in $r$-uniform, $n$-vertex hypergraphs without Berge paths on $k$ vertices. The extremal examples for their bounds are disconnected hypergraphs in which each component has either too few edges or too few vertices to contain such a Berge path. We consider the setting in which the host hypergraph is connected. Let $\\operatorname{ex}^{\\mathrm{conn}}_r(n,\\mathcal{BP}_k)$ denote the maximum number of edges in an $n$-vertex, $r$-uniform, connected hypergraph that does not contain a Berge path on $k$ vertices. This number was determined by Zhang, Broersma, Győri, Tompkins, Wang for $k \\leq r+2$, and Zhao, Gerbner, Zhou for $k \\geq 2r+2$. In this paper, we resolved the remaining cases $r+3 \\leq k \\leq 2r+1$ when $n$ is sufficiently large, confirming a conjecture of Zhang, et al.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32875",
  "author_total": 2,
  "authors": [
    {
      "name": "Yupei Li"
    },
    {
      "name": "Ruth Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajwy8181v09vj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32875",
  "fulltext_url": null,
  "id": "ajwy8181v09vj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32875",
  "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": "W7223690729",
  "pdf_url": "https://arxiv.org/pdf/2610.32875",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajwy8181v09vj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:43Z",
      "native_id": "2610.32875",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Turán number of Berge paths in connected hypergraphs",
  "title_text": "The Turán number of Berge paths in connected hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:43Z",
  "url": "https://research.draconitic.com/paper/ajwy8181v09vj",
  "venue": "arXiv",
  "versions": []
}