{
  "abstract": "A digraph $D = (V,E)$ is 3-transitive (respectively, 3-quasi-transitive) if whenever $(u,v,w,z)$ is a directed path of length 3, $(u,z) \\in E$ (respectively, $(u,z) \\in E$ or $(z,u) \\in E$). These digraphs extend the concepts of transitive and quasi-transitive digraphs, respectively. For 3-transitive and 3-quasi-transitive digraphs, only the strong case has been characterized. In this paper, we introduce the notion of semi-acyclic digraphs and use it to describe completely the structure of 3-transitive and 3-quasi-transitive digraphs. As an application of this type of structure description, we prove that the path partition conjecture holds for the class of extended semi-acyclic digraphs, which generalizes two previously known results on the conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14217",
  "author_total": 2,
  "authors": [
    {
      "name": "Shamik Ghosh"
    },
    {
      "name": "Jing Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0k6hymm3089d4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14217",
  "fulltext_url": null,
  "id": "0k6hymm3089d4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14217",
  "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": "W7221831809",
  "pdf_url": "https://arxiv.org/pdf/2610.14217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0k6hymm3089d4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14217"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Path Partition Conjecture and 3-(quasi-)Transitive Digraphs",
  "title_text": "The Path Partition Conjecture and 3-(quasi-)Transitive Digraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/0k6hymm3089d4",
  "venue": "arXiv",
  "versions": []
}