{
  "id": "2505.09809",
  "version": "v1",
  "published": "2025-05-14T21:23:06.000Z",
  "updated": "2025-05-14T21:23:06.000Z",
  "title": "On Alternating 6-Cycles in Edge-Coloured Graphs",
  "authors": [
    "Hao Chen",
    "Jonathan A. Noel"
  ],
  "comment": "19 pages, 2 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "In this short note, we use flag algebras to prove that the number of colour alternating 6-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniformly random colouring. This settles the first open case of a problem of Basit, Granet, Horsley, K\\\"undgen and Staden.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-14T21:23:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "edge-coloured graphs",
      "alternating",
      "first open case",
      "short note",
      "flag algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}