{
  "abstract": "Given a sequence $\\mathbf{a}=(a_i)_{i\\geq 1}$ of positive real numbers, we say that a colouring $c:E(K_n)\\to \\mathbb{N}$ is $\\mathbf{a}$-bounded if the proportion of edges coloured $i$ is at most $a_i$, for all $i$. We write \\[ \\mathbf{a}\\, \\to\\, K_k \\] if, for all sufficiently large $n$, all $\\mathbf{a}$-bounded colourings $c:E(K_n)\\to \\mathbb{N}$ contain a monochromatic $K_k$. We say that the sequence $\\mathbf{a}$ is \\emph{Decay-Ramsey} if $\\mathbf{a}\\to K_k$ for all $k\\ge 2$. In this short paper we introduce the question of determining which sequences are Decay-Ramsey and present some initial results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20577",
  "author_total": 4,
  "authors": [
    {
      "name": "Francesco Di Braccio"
    },
    {
      "name": "Simon Griffiths"
    },
    {
      "name": "Pedram Noohi"
    },
    {
      "name": "Leo Versteegen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cj1ksjx4dvd7c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20577",
  "fulltext_url": null,
  "id": "cj1ksjx4dvd7c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20577",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7222160607",
  "pdf_url": "https://arxiv.org/pdf/2610.20577",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cj1ksjx4dvd7c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20577",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20577"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Decay-Ramsey Sequences",
  "title_text": "Decay-Ramsey Sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/cj1ksjx4dvd7c",
  "venue": "arXiv",
  "versions": []
}