{
  "id": "2306.13014",
  "version": "v1",
  "published": "2023-06-22T16:23:21.000Z",
  "updated": "2023-06-22T16:23:21.000Z",
  "title": "The binomial random graph is a bad inducer",
  "authors": [
    "Vishesh Jain",
    "Marcus Michelen"
  ],
  "comment": "4 pages; comments welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a finite graph $F$ and a value $p \\in [0,1]$, let $I(F,p)$ denote the largest $y$ for which there is a sequence of graphs of edge density approaching $p$ so that the induced $F$-density of the sequence approaches $y$. In this short note, we show that for all $F$ on at least three vertices and $p \\in (0,1)$, the binomial random graph $G(n,p)$ has induced $F$-density strictly less than $I(F,p).$ This provides a negative answer to a problem posed by Liu, Mubayi and Reiher.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-22T16:23:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "binomial random graph",
      "bad inducer",
      "finite graph",
      "sequence approaches",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}