{
  "abstract": "Stein conjectured that for every positive integer $k$, every oriented graph with minimum semi-degree greater than $k/2$ contains every oriented path of length $k$ [Springer Optim.Appl. 165 (2020), 459--486]. For directed paths this is a classical result of Jackson (1981). The two-block case of the conjecture was established by Chen, Hou and Zhou (2025). In this paper we prove the two-block analogue of Jackson's theorem. For all positive integers $s$ and $r$, let $P(s,r)$ be the oriented path consisting of two directed paths of lengths $s$ and $r$ with a common terminal vertex, and let $Q(s,r)$ be its reverse. We show that for all $K\\ge3$ and all $s,r\\ge1$ with $s+r\\le K$, every oriented graph $D$ with $δ(D)\\ge K$ and $d_D^+(u)+d_D^-(v)\\ge K-1$ for every ordered pair of distinct vertices $(u,v)\\notin A(D)$ contains both $P(s,r)$ and $Q(s,r)$. Our result is the two-block analogue of Jackson's theorem, and it extends the two-block result of Chen, Hou and Zhou. The proof iterates a shift of the terminal vertex of a longest path.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04691",
  "author_total": 3,
  "authors": [
    {
      "name": "Ke Zhao"
    },
    {
      "name": "Jia Zhou"
    },
    {
      "name": "Yunshu Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2td3cepb590x4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04691",
  "fulltext_url": null,
  "id": "2td3cepb590x4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04691",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2td3cepb590x4.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Two-block paths in oriented graphs under the Ore-type condition",
  "title_text": "Two-block paths in oriented graphs under the Ore-type condition",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/2td3cepb590x4",
  "venue": "arXiv",
  "versions": []
}