{
  "abstract": "Given $r \\in \\mathbb{N}$ and an edge-coloured complete graph such that the average number of colours incident with a vertex is at most $r$, Conlon and Stein asked whether there is a vertex partition into a bounded number of monochromatic cycles, and proved this for $r=2$. We settle the first open case by proving the corresponding statement for $r=3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.29336",
  "author_total": 7,
  "authors": [
    {
      "name": "Csaba Biró"
    },
    {
      "name": "Richard Lang"
    },
    {
      "name": "Ryan R. Martin"
    },
    {
      "name": "Guilherme Oliveira Mota"
    },
    {
      "name": "Alexey Pokrovskiy"
    },
    {
      "name": "Miklós Ruszinkó"
    },
    {
      "name": "Gábor N. Sárközy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7mtz51hhq4jxr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.29336",
  "fulltext_url": null,
  "id": "7mtz51hhq4jxr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.29336",
  "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": "W7172321788",
  "pdf_url": "https://arxiv.org/pdf/2607.29336",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7mtz51hhq4jxr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.29336",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.29336"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Monochromatic cycle partitions in 3-mean edge-colourings",
  "title_text": "Monochromatic cycle partitions in 3-mean edge-colourings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7mtz51hhq4jxr",
  "venue": "arXiv",
  "versions": []
}