{
  "abstract": "For ordered graphs $H_1,\\ldots,H_t$, let $\\rt(H_1,\\ldots,H_t)$ denote the least integer $N$ such that every $t$-coloring of the edges of the naturally ordered complete graph on $[N]$ contains an ordered copy of $H_i$ in color $i$ for some $i\\in[t]$. We prove that a uniformly random ordered matching $M$ on $n$ vertices with interval chromatic number two asymptotically almost surely satisfies \\[ \\rt(K_3,M) =Ω\\left(\\frac{n^{4/3}}{(\\log n)^{1/3}}\\right). \\] This strengthens the lower bound $Ω((n/\\log n)^{5/4})$ of Balko and Poljak for such random matchings and improves the general existential lower bound of Conlon, Fox, Lee and Sudakov by a factor of $\\log n$. The proof combines pseudorandom triangle-free graphs, a coarse encoding of order-preserving embeddings, and a permutation avoidance estimate derived from Brègman's inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19632",
  "author_total": 3,
  "authors": [
    {
      "name": "Wen Chen"
    },
    {
      "name": "Qizhong Lin"
    },
    {
      "name": "Chunlin You"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jf4f3qv2k6re.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19632",
  "fulltext_url": null,
  "id": "7jf4f3qv2k6re",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19632",
  "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": "W7213602569",
  "pdf_url": "https://arxiv.org/pdf/2609.19632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jf4f3qv2k6re.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19632"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Ordered matchings versus triangles via pseudorandom triangle-free graphs",
  "title_text": "Ordered matchings versus triangles via pseudorandom triangle-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/7jf4f3qv2k6re",
  "venue": "arXiv",
  "versions": []
}