{
  "abstract": "Smith's conjecture asserts that in every $k$-connected graph with $k\\geq 2$, any two longest cycles intersect in at least $k$ vertices. In this work, we establish an $Ω(k^{8/11})$ bound for this conjecture, improving upon the $Ω(k^{2/3})$ bound of Ma and Zhao. Our proof combines a Ramsey theoretic refinement of the traditional Turán-type approach with computer search.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30353",
  "author_total": 1,
  "authors": [
    {
      "name": "Douglas M. Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4qn60mza1apdw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30353",
  "fulltext_url": null,
  "id": "4qn60mza1apdw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30353",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7204902894",
  "pdf_url": "https://arxiv.org/pdf/2608.30353",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4qn60mza1apdw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30353",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30353"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Improved Bound for Smith's Longest Cycles Conjecture via a Forbidden Subdivision",
  "title_text": "An Improved Bound for Smith's Longest Cycles Conjecture via a Forbidden Subdivision",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/4qn60mza1apdw",
  "venue": "arXiv",
  "versions": []
}