{
  "abstract": "We study representations for relation algebras corresponding to certain edge colourings of complete graphs. Previously suitable colourings were obtained for the number of colours $n$ up to $2000$, with two exceptions: $n = 8$ and $n = 13$. Using a method that we have called the FBF (Fusion Beautiful Fusions) method, we find colourings for $8$ and $13$ colours. Our method is a new guess-and-check approach that we describe as an adaptation of Comer's finite-field method. Using FBF we construct novel colourings that are non-isomorphic to existing published colourings for 5, 6, 7, 9, 10, 11 and 12 colours.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26851",
  "author_total": 4,
  "authors": [
    {
      "name": "Charles Gretton"
    },
    {
      "name": "Tomasz Kowalski"
    },
    {
      "name": "Richard Pennifold"
    },
    {
      "name": "Cody Christopher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0cfg75j6zqw79.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26851",
  "fulltext_url": null,
  "id": "0cfg75j6zqw79",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26851",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214228425",
  "pdf_url": "https://arxiv.org/pdf/2609.26851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0cfg75j6zqw79.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A New Method that can Generate Ramsey Colourings for Eight and Thirteen Colours",
  "title_text": "A New Method that can Generate Ramsey Colourings for Eight and Thirteen Colours",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0cfg75j6zqw79",
  "venue": "arXiv",
  "versions": []
}