{
  "abstract": "Let \\(β(G)\\) denote the minimum size of a feedback edge set of a digraph \\(G\\), and let \\(γ(G)\\) denote the number of unordered pairs of nonadjacent vertices. Motivated by the Chudnovsky--Seymour--Sullivan conjecture for \\(3\\)-free digraphs, we study the corresponding feedback-edge problem for bipartite digraphs. In the bipartite setting, \\(γ(G)\\) is taken to count only nonadjacent pairs with ends in distinct partite sets. We prove that every \\(4\\)-free bipartite digraph \\(G\\) satisfies \\(β(G)\\le γ(G)/2\\). We also determine the exact Turán number of \\(2k\\)-free strong bipartite digraphs with partite sets \\(X\\) and \\(Y\\): if \\(|X|,|Y|\\ge k+1\\), then the maximum number of edges is $$(|X|-(k-1))(|Y|-(k-1))+2k-2.$$ Finally, for the extremal case \\(k=2\\), we analyze the structure of \\(4\\)-free strong bipartite Turán digraphs and prove the sharper bound \\(β(G)\\le γ(G)/3\\) for all such digraphs. This constant is attained by a natural balanced three-block construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06462",
  "author_total": 3,
  "authors": [
    {
      "name": "Bin Chen"
    },
    {
      "name": "Jianfeng Hou"
    },
    {
      "name": "Siyue Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r708qz9h2c4f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06462",
  "fulltext_url": null,
  "id": "3r708qz9h2c4f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06462",
  "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": "W7212008724",
  "pdf_url": "https://arxiv.org/pdf/2609.06462",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r708qz9h2c4f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06462",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06462"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Feedback edge set in bipartite digraph",
  "title_text": "Feedback edge set in bipartite digraph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3r708qz9h2c4f",
  "venue": "arXiv",
  "versions": []
}