{
  "abstract": "The Ramsey number $r(H)$ of a graph $H$ is the minimum positive integer $N$ such that every red/blue edge-coloring of the complete graph $K_N$ on $N$ vertices contains a monochromatic copy of $H$. The Ramsey multiplicity $M(H,n)$ is the minimum number of monochromatic copies of $H$ over all red/blue edge-colorings of $K_n$. It is called threshold Ramsey multiplicity if $n=r(H)$, and denoted by $m(H)$. The only previously known general infinite family for which $m(H)$ has been determined is stars, due to Harary and Prins (1974). Let $C_k$ denote a cycle on $k$ vertices. Conlon, Fox, Sudakov, and Wei (2022) conjectured that $m(C_k)=(k-1)!/2$ for every sufficiently large odd integer $k$. In this paper, we determine $M(C_k,r(C_k)+\\ell)$ for every fixed nonnegative integer $\\ell$ and all sufficiently large odd $k$, and characterize all extremal colorings, thereby confirming the conjecture. This is also a second general infinite family for which $m(H)$ has been determined.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07285",
  "author_total": 4,
  "authors": [
    {
      "name": "Ting Huang"
    },
    {
      "name": "Junying Lu"
    },
    {
      "name": "Jiabao Yang"
    },
    {
      "name": "Yaojun Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e141fzrr925d1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07285",
  "fulltext_url": null,
  "id": "e141fzrr925d1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07285",
  "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": "W7212070141",
  "pdf_url": "https://arxiv.org/pdf/2609.07285",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e141fzrr925d1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.07285",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07285"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Ramsey multiplicity and extremal colorings for odd cycles",
  "title_text": "Ramsey multiplicity and extremal colorings for odd cycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/e141fzrr925d1",
  "venue": "arXiv",
  "versions": []
}