{
  "id": "2209.15493",
  "version": "v1",
  "published": "2022-09-30T14:29:41.000Z",
  "updated": "2022-09-30T14:29:41.000Z",
  "title": "Rainbow triangles in families of triangles",
  "authors": [
    "Ido Goorevitch",
    "Ron Holzman"
  ],
  "comment": "6 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that a family $\\mathcal{T}$ of distinct triangles on $n$ given vertices that does not have a rainbow triangle (that is, three edges, each taken from a different triangle in $\\mathcal{T}$, that form together a triangle) must be of size at most $\\frac{n^2}{8}$. We also show that this result is sharp and characterize the extremal case. In addition, we discuss a version of this problem in which the triangles are not necessarily distinct, and show that in this case, the same bound holds asymptotically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-30T14:29:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "rainbow triangle",
      "distinct triangles",
      "extremal case",
      "bound holds",
      "necessarily distinct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}