{
  "id": "2407.14084",
  "version": "v1",
  "published": "2024-07-19T07:38:57.000Z",
  "updated": "2024-07-19T07:38:57.000Z",
  "title": "A Purely Entropic Approach to the Rainbow Triangle Problem",
  "authors": [
    "Ting-Wei Chao",
    "Hung-Hsun Hans Yu"
  ],
  "comment": "5 pages, 5 figures",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "In this short note, we present a purely entropic proof that in a $3$-edge-colored simple graph with $R$ red edges, $G$ green edges, and $B$ blue edges, the number of rainbow triangles is at most $\\sqrt{2RGB}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-19T07:38:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05D40",
      "94A17"
    ],
    "keywords": [
      "rainbow triangle problem",
      "purely entropic approach",
      "short note",
      "green edges",
      "purely entropic proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}