{
  "abstract": "The Ramsey number R(s,t) is the least integer n such that any coloring of the edges of Kn with two colors produces either a monochromatic Ks in one color or a monochromatic Kt in the other. If s=t, we call R(s,s) a diagonal Ramsey number. The threshold Ramsey multiplicity of a diagonal Ramsey number R(s,s), denoted by m(s,s) or m2(s), is the smallest number of copies of a monochromatic Ks that can be found in any coloring of the edges of KR(s,s). For instance, m2(2)=1, m2(3)=2, and m2(4)=9. We derive upper bounds for multicolor, off-diagonal threshold Ramsey multiplicities. In the diagonal two-color case, the resulting explicit numerical bounds improve those obtained from the elementary random-coloring estimate for 5≤s≤8. In the multicolor case, we recover the known value m(3,3,3)=5 and obtain the bound m(3,3,4)≤8. We conclude with a general framework for seeking further improvements.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, University of North Dakota, Grand Forks, ND 58202, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Bryce Alan Christopherson",
      "orcid": "0000-0002-4389-8709"
    },
    {
      "affs": [
        0
      ],
      "name": "Casia Steinhaus",
      "orcid": "0009-0008-9261-446X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c843c1sj19a40.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193553",
  "fulltext_url": null,
  "id": "c843c1sj19a40",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3553",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W4407093074",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/c843c1sj19a40.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193553",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Limits and Structures in Graph Theory",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bounds on the Threshold Ramsey Multiplicity of Ramsey Numbers with Many Colors",
  "title_text": "Bounds on the Threshold Ramsey Multiplicity of Ramsey Numbers with Many Colors",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/c843c1sj19a40",
  "venue": "Mathematics",
  "versions": []
}