{
  "abstract": "For a graph $F$, the Turán number $\\operatorname{ex}(n,F)$ is the maximum number of edges in an $n$-vertex graph containing no copy of $F$. Determining the Turán numbers of even cycles is a central problem in extremal graph theory and remains open in general. For $C_6$, the best previous upper bound was due to Füredi, Naor, and Verstraëte [Advances in Mathematics, 2006], who proved that, for sufficiently large positive integer $n$, $$ \\operatorname{ex}(n,C_6) \\leq λn^{4/3}+O(n)<0.6272 n^{4/3}, $$ where $λ$ is the real root of $ 16λ^3-4λ^2+λ-3=0$. We improve this bound by showing that, for sufficiently large positive integer $n$, $$ \\operatorname{ex}(n,C_6) \\leq αn^{4/3}+O(n)<0.6144 n^{4/3}, $$ where $α$ is the unique real root of $ 4 α^{3} (3/2)^{1-1/(2α)} =1$ in the interval $(1/2,2/3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10003",
  "author_total": 4,
  "authors": [
    {
      "name": "Sandip Das"
    },
    {
      "name": "Sk Samim Islam"
    },
    {
      "name": "Aashirwad Mohapatra"
    },
    {
      "name": "Saumya Sen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5nz62ah2mzn8r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10003",
  "fulltext_url": null,
  "id": "5nz62ah2mzn8r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10003",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7212144084",
  "pdf_url": "https://arxiv.org/pdf/2609.10003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5nz62ah2mzn8r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10003"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Improved Upper Bound for the Turán Number of the Hexagon",
  "title_text": "An Improved Upper Bound for the Turán Number of the Hexagon",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/5nz62ah2mzn8r",
  "venue": "arXiv",
  "versions": []
}