{
  "abstract": "Cycle rank is a depth parameter for digraphs introduced by Eggan in 1963. Gruber (DMTCS 2012) and Giannopoulou, Hunter, and Thilikos (DAM 2012) asked whether the problem of determining if a given digraph has cycle rank at most $w$ is fixed-parameter tractable parameterized by $w$. We provide such algorithms for semi-complete digraphs, and for digraphs of bounded directed clique-width. Specifically, we show that given an $n$-vertex semi-complete digraph~$G$ and an integer $w$, one can in time $2^{\\mathcal{O}((w+1)4^{w})} n^2$ determine whether $G$ has cycle rank at most~$w$. The proof is reduced to the case of bounded directed clique-width, and we then show that given an $n$-vertex digraph $G$ with a directed clique-width $k$-expression and an integer $w$, one can in time $2^{\\mathcal{O}((w+1)4^k)}n$ determine whether $G$ has cycle rank at most $w$. Additionally, we consider the \\textsc{Minimum Feedback Arc Set} problem on semi-complete digraphs, and show that it can be solved in time $n^{\\mathcal{O}(w)}$, when a cycle rank decomposition of depth $w\\ge 1$ is given.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29336",
  "author_total": 3,
  "authors": [
    {
      "name": "Seokbeom Kim"
    },
    {
      "name": "O-joung Kwon"
    },
    {
      "name": "Myounghwan Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bhj1zedf6548g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29336",
  "fulltext_url": null,
  "id": "bhj1zedf6548g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29336",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7166651690",
  "pdf_url": "https://arxiv.org/pdf/2606.29336",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bhj1zedf6548g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2606.29336",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29336"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An FPT algorithm for cycle rank on semi-complete digraphs",
  "title_text": "An FPT algorithm for cycle rank on semi-complete digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/bhj1zedf6548g",
  "venue": "arXiv",
  "versions": []
}