{
  "abstract": "We prove that, for every $k\\ge2$ and every sufficiently large odd $n$, the induced size--Ramsey number of $C_n$ satisfies \\[ \\widehat R_{\\mathrm{ind}}(C_n;k)=e^{Θ(k)}n. \\] This improves the previous upper bound of $e^{O(k\\log k)}n$ and resolves a conjecture of Bradač, Draganić and Sudakov. We obtain this result by proving a stronger form of their odd-hole gadget conjecture: we construct a graph with $e^{O(k)}$ edges whose every $k$-edge-colouring contains a monochromatic induced odd cycle of length $O(\\log k)$. Our proof develops a spread-based approach to finding induced cycles. The key idea is to place spread probability weights directly on families of candidate cycles and control their possible chords through a quadratic chord score. Combining this with random sparsification and hypergraph containers yields a sparse host graph that works for every $k$-edge-colouring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06481",
  "author_total": 2,
  "authors": [
    {
      "name": "Lanchao Wang"
    },
    {
      "name": "Xiaolin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ac7gnk63hxxr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06481",
  "fulltext_url": null,
  "id": "3ac7gnk63hxxr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06481",
  "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": "W7212061737",
  "pdf_url": "https://arxiv.org/pdf/2609.06481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ac7gnk63hxxr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.06481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Induced Size-Ramsey Numbers of Odd Cycles via Spread Measures",
  "title_text": "Induced Size-Ramsey Numbers of Odd Cycles via Spread Measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3ac7gnk63hxxr",
  "venue": "arXiv",
  "versions": []
}