{
  "abstract": "For every real $t>0$, we prove that every $2$-connected $t$-tough graph contains a cycle of length at least $\\ell$ whenever $n \\leq \\ell(1 + 1/t)^{\\lfloor \\ell/2\\rfloor - 1}$. This establishes the logarithmic bound conjectured by Broersma, van den Heuvel, Jung, and Veldman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16083",
  "author_total": 2,
  "authors": [
    {
      "name": "Levi Segal"
    },
    {
      "name": "Jacques Verstraete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fzv7vy0nfwdjm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16083",
  "fulltext_url": null,
  "id": "fzv7vy0nfwdjm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16083",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7213438220",
  "pdf_url": "https://arxiv.org/pdf/2609.16083",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fzv7vy0nfwdjm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.16083",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16083"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Logarithmic Circumference In Tough Graphs",
  "title_text": "Logarithmic Circumference In Tough Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/fzv7vy0nfwdjm",
  "venue": "arXiv",
  "versions": []
}