{
  "abstract": "The \\emph{ordered Ramsey number} $r_<(G,H)$ of ordered $k$-graphs $G$ and $H$ is the least integer $N$ such that every red-blue edge-coloring of the naturally ordered complete $k$-graph on $[N]$ contains a blue ordered copy of $G$ or a red ordered copy of $H$. We prove that there is an absolute constant $c>0$ such that, for every integer $d\\ge1$, there is a constant $C_d>0$ for which every weakly $d$-degenerate ordered $3$-graph $H$ on $t$ vertices satisfies \\[ r_<\\bigl(H,K_3^{(3)}(n)\\bigr) \\le t\\,2^{C_d n^{2-c/d}} \\] for every positive integer $n$. This resolves a problem posed by Balko and Vizer ({\\em SIAM J. Discrete Math., 2022}) in a stronger form. Furthermore, we show that the weak-degeneracy hypothesis cannot be replaced by bounded standard degeneracy. In particular, for every sufficiently large $n$, there exists a $1$-degenerate ordered $3$-graph $F$ on at most $2^{O(n)}$ vertices such that $r_<\\bigl(F,K_3^{(3)}(n)\\bigr)>2^{Ω(n^2)}.$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16767",
  "author_total": 4,
  "authors": [
    {
      "name": "Wen Chen"
    },
    {
      "name": "Zihan He"
    },
    {
      "name": "Qizhong Lin"
    },
    {
      "name": "Meng Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0h1dys3ze505q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16767",
  "fulltext_url": null,
  "id": "0h1dys3ze505q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16767",
  "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": "W7213401947",
  "pdf_url": "https://arxiv.org/pdf/2609.16767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0h1dys3ze505q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Ordered Ramsey numbers of 3-uniform hypergraphs with bounded weak degeneracy",
  "title_text": "Ordered Ramsey numbers of 3-uniform hypergraphs with bounded weak degeneracy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/0h1dys3ze505q",
  "venue": "arXiv",
  "versions": []
}