{
  "abstract": "Let $t \\ge 1$ be an integer, and let $G$ be a $t$-tough $n$-vertex graph with degree sequence $d_1, d_2, \\ldots, d_n$ in non-decreasing order. In 1995, Hoàng conjectured that if $G$ is Hamiltonian and, for every integer $i$ satisfying $t\\le i<n/2$, $d_i\\le i$, and $d_{n-i+t}<n-i$, one has $d_j + d_{n-j+t} \\ge n$ for all $j$ with $i < j < \\frac{n}{2}$, then $G$ is pancyclic or bipartite. In this paper, we disprove the conjecture for $t = 1$ and confirm it for all $t \\ge 7$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23107",
  "author_total": 2,
  "authors": [
    {
      "name": "Songling Shan"
    },
    {
      "name": "Zachary Warren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/024afnx0a3782.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23107",
  "fulltext_url": null,
  "id": "024afnx0a3782",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23107",
  "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": "W7214025212",
  "pdf_url": "https://arxiv.org/pdf/2609.23107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/024afnx0a3782.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Degree sequence condition for pancyclicity in tough graphs",
  "title_text": "Degree sequence condition for pancyclicity in tough graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/024afnx0a3782",
  "venue": "arXiv",
  "versions": []
}