{
  "abstract": "A digraph is antidirected if every vertex has indegree zero or outdegree zero. Let $k\\ge2$, and let $F$ be an antidirected forest with $k$ arcs and no isolated vertices. We prove that every digraph $D$ of order $n$ with more than $g_k(n):=2\\max\\left\\{\\binom{2k-1}{2}, (k-1)\\left(n-\\frac{k}{2}\\right)\\right\\}$ arcs contains $F$ as a subdigraph. For $n\\ge2k-1$, this threshold equals $2\\mathrm{ex}(n,kK_2)$ and is attained by symmetric digraphs arising from extremal $kK_2$-free graphs. Consequently, the maximum directed extremal number over all such forests is $2\\mathrm{ex}(n,kK_2)$. The proof combines a counting inequality for rooted antidirected forests, embeddings extending vertex-disjoint arcs, and vertex deletion. In the remaining case, the Gallai--Edmonds decomposition of the underlying graph gives the required bound on the number of arcs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18469",
  "author_total": 2,
  "authors": [
    {
      "name": "Gengtao Liu"
    },
    {
      "name": "Yunshu Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2eg0253kcfmsy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18469",
  "fulltext_url": null,
  "id": "2eg0253kcfmsy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18469",
  "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": "W7213497434",
  "pdf_url": "https://arxiv.org/pdf/2609.18469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2eg0253kcfmsy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Antidirected forests in digraphs",
  "title_text": "Antidirected forests in digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/2eg0253kcfmsy",
  "venue": "arXiv",
  "versions": []
}