{
  "abstract": "For a digraph $D$, let $α_2(D)$ be the largest size of a vertex set containing no directed $2$-cycle. Let $f_2(a)$ be the least positive integer $k$ such that every $k$-strongly connected digraph $D$ with $α_2(D)\\le a$ has a Hamilton cycle. Jackson and Ordaz conjectured that $f_2(a)\\le a+1$. Towards this conjecture, we establish the near-linear bound $f_2(a)=O\\!\\left(\\frac{a(\\log a)^4}{(\\log\\log a)^2}\\right),$ and hence $f_2(a)=O_\\varepsilon(a^{1+\\varepsilon})$ for every fixed $\\varepsilon>0$. We also disprove the pancyclicity conjecture of Jackson and Ordaz that every digraph $D$ with $κ(D)\\geα_2(D)+1$ contains a directed cycle of every length from $2$ to $|V(D)|$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10292",
  "author_total": 2,
  "authors": [
    {
      "name": "Chengli Li"
    },
    {
      "name": "Bo Ning"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bnbxz2kh3dvje.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10292",
  "fulltext_url": null,
  "id": "bnbxz2kh3dvje",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10292",
  "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": "W7220932145",
  "pdf_url": "https://arxiv.org/pdf/2610.10292",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bnbxz2kh3dvje.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10292",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10292"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A near-linear Chvátal--Erdős condition for Hamilton cycles in digraphs",
  "title_text": "A near-linear Chvátal--Erdős condition for Hamilton cycles in digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/bnbxz2kh3dvje",
  "venue": "arXiv",
  "versions": []
}