{
  "abstract": "For every rational number $γ>1$, we construct a fixed bipartite graph $H_γ$ such that $r_k(H_γ;K_N)=Θ_{γ,k}((N/\\log N)^γ)$ for every fixed $k\\ge 3$. Here $r_k(H;K_N)=r(H,\\ldots,H,K_N)$, with $k$ copies of $H$. The lower bound uses a symmetric random algebraic graph which avoids a fixed rooted power and has sufficiently strong local density for the Alon-Rodl method. The main algebraic step establishes a nonzero obstruction within the full symmetric coefficient space; the upper bound uses the rooted graphs from the proof of the rational exponents conjecture. We also obtain induced even-cycle asymptotics in the same construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26061",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vcvz907p170d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26061",
  "fulltext_url": null,
  "id": "2vcvz907p170d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26061",
  "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": "W7223010824",
  "pdf_url": "https://arxiv.org/pdf/2610.26061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2vcvz907p170d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Single-graph rational exponents in mixed multicolour Ramsey theory",
  "title_text": "Single-graph rational exponents in mixed multicolour Ramsey theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2vcvz907p170d",
  "venue": "arXiv",
  "versions": []
}