{
  "abstract": "A majority edge-colouring of a graph $G$ is a colouring of the edges of $G$ such that, for every vertex $v$ of $G$, at most half of the edges incident with $v$ receive the same colour. This notion was introduced by Bock et al. in 2023, who proved that every graph of minimum degree at least $2$ has a majority $4$-edge-colouring. We investigate an on-line variant of majority edge-colouring in which the graph is revealed by the Presenter edge-by-edge and the Algorithm must colour each edge immediately and irrevocably. In particular. we prove that the greedy strategy, which uses at most five colours, is optimal among on-line algorithms if $δ= O(\\frac{\\log n}{\\log\\log n})$. We further extend our results to $1/k$-majority edge-colourings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37973",
  "author_total": 1,
  "authors": [
    {
      "name": "Paweł Pękała"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zvmxeb6wxbsv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37973",
  "fulltext_url": null,
  "id": "4zvmxeb6wxbsv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37973",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7214965320",
  "pdf_url": "https://arxiv.org/pdf/2609.37973",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zvmxeb6wxbsv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37973",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37973"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On-line majority edge-colourings of graphs",
  "title_text": "On-line majority edge-colourings of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4zvmxeb6wxbsv",
  "venue": "arXiv",
  "versions": []
}