{
  "abstract": "For two digraph properties $P_1$ and $P_2$, a $(P_1,P_2)$-arc-decomposition of a digraph $D$ is a partition $A(D)=A_1\\mathbin{\\dot\\cup}A_2$ such that the spanning subdigraphs $D[A_1]$ and $D[A_2]$ have properties $P_1$ and $P_2$, respectively. We prove that it is NP-complete to decide whether a digraph admits an arc-decomposition with properties $(P_1,P_2)$ where $(P_1,P_2)\\in \\{$(perfect matching, having no odd cycle), (perfect matching, strong), (perfect matching, having an out-branching), (cycle factor, having no odd cycle)$\\}$. All four problems remain NP-complete even when restricted to strongly connected digraphs. We also prove that every strongly connected digraph with minimum semi-degree at least three contains two vertex-disjoint cycles whose simultaneous arc deletion leaves the digraph strongly connected. These results settle some open problems posed by Bang-Jensen, Bessy, Gonçalves, and Picasarri-Arrieta [Theoret. Comput. Sci. 928 (2022), 167--182].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24031",
  "author_total": 4,
  "authors": [
    {
      "name": "Hangning Liu"
    },
    {
      "name": "Jørgen Bang-Jensen"
    },
    {
      "name": "Jin Yan"
    },
    {
      "name": "Jia Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7wbzfnp4kgrvc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24031",
  "fulltext_url": null,
  "id": "7wbzfnp4kgrvc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24031",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7204500132",
  "pdf_url": "https://arxiv.org/pdf/2608.24031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7wbzfnp4kgrvc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2608.24031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors",
  "title_text": "Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7wbzfnp4kgrvc",
  "venue": "arXiv",
  "versions": []
}