{
  "abstract": "For a digraph $D$, let $α_2(D)$ be the largest size of a vertex set no two of whose vertices lie in a common directed $2$-cycle. Let $f_2(a)$ be the least integer $K$ such that every $K$-connected digraph $D$ with $α_2(D)\\le a$ has a Hamilton cycle. Jackson proved in 1987 that $f_2(a)\\le2^a(a+2)!$, whereas a conjecture of Jackson and Ordaz predicts $f_2(a)\\le a+1$. We prove the quadratic bound $f_2(a)\\le12000a^2$. We also prove that $κ(H)\\ge6000(α(H)+r)$ guarantees vertex-disjoint paths joining any prescribed $r$ pairs of distinct vertices and covering $V(H)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.08401",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiangdong Ai"
    },
    {
      "name": "Yongtang Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mb34me6qb37v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.08401",
  "fulltext_url": null,
  "id": "5mb34me6qb37v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.08401",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7163984071",
  "pdf_url": "https://arxiv.org/pdf/2606.08401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mb34me6qb37v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2606.08401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.08401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A quadratic refinement of Jackson's \\CE\\ condition for Hamilton cycles in digraphs",
  "title_text": "A quadratic refinement of Jackson's \\CE\\ condition for Hamilton cycles in digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5mb34me6qb37v",
  "venue": "arXiv",
  "versions": []
}