{
  "id": "2204.07567",
  "version": "v1",
  "published": "2022-04-15T17:40:52.000Z",
  "updated": "2022-04-15T17:40:52.000Z",
  "title": "Some remarks on graphs without rainbow triangles",
  "authors": [
    "Ervin Győri",
    "Zhen He",
    "Zequn Lv",
    "Nika Salia",
    "Casey Tompkins",
    "Kitti Varga",
    "Xiutao Zhu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given graphs $G_1$, $G_2$ and $G_3$ on a common vertex set of size $n$, a rainbow triangle is a triangle consisting of one edge from each $G_i$. In this note we provide a counterexample to a conjecture of Frankl on the maximum product of the sizes of the edge sets of three graphs avoiding a rainbow triangle. Moreover we propose an alternative conjecture and prove it in the case when every pair is an edge in at least one of the graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-15T17:40:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rainbow triangle",
      "common vertex set",
      "maximum product",
      "edge sets",
      "counterexample"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}