{
  "abstract": "Let $D$ be a finite simple minimally strongly $k$-connected digraph, where $k\\ge 2$, and let $n=|V(D)|$. Mader proved in 1985 that $|A(D)|\\le 2k(n-k)$ for all sufficiently large $n$, with equality if and only if $D\\cong \\overleftrightarrow{K}_{k,n-k}$ (JCTB 1985). We prove that this bound holds whenever $n\\ge 3k-1$ and that the order threshold $3k-1$ is best possible. Moreover, if $n\\ge 3k$, then equality holds if and only if $D\\cong \\overleftrightarrow{K}_{k,n-k}$. The threshold $3k$ is also best possible. These results resolve the conjecture of Mader in (JCTB 1985).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14979",
  "author_total": 4,
  "authors": [
    {
      "name": "Junran Yu"
    },
    {
      "name": "Gregory Gutin"
    },
    {
      "name": "Hong-Jian Lai"
    },
    {
      "name": "Xiaoyan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0eabxve95237q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14979",
  "fulltext_url": null,
  "id": "0eabxve95237q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14979",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7221770143",
  "pdf_url": "https://arxiv.org/pdf/2610.14979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0eabxve95237q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sharp bounds and extremal structure of minimally strongly $k$-connected digraphs",
  "title_text": "Sharp bounds and extremal structure of minimally strongly k-connected digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0eabxve95237q",
  "venue": "arXiv",
  "versions": []
}