{
  "id": "2409.05931",
  "version": "v1",
  "published": "2024-09-09T12:10:38.000Z",
  "updated": "2024-09-09T12:10:38.000Z",
  "title": "Infinitely many minimally Ramsey size-linear graphs",
  "authors": [
    "Yuval Wigderson"
  ],
  "comment": "2 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $G$ is said to be Ramsey size-linear if $r(G,H) =O_G (e(H))$ for every graph $H$ with no isolated vertices. Erd\\H{o}s, Faudree, Rousseau, and Schelp observed that $K_4$ is not Ramsey size-linear, but each of its proper subgraphs is, and they asked whether there exist infinitely many such graphs. In this short note, we answer this question in the affirmative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-09T12:10:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimally ramsey size-linear graphs",
      "proper subgraphs",
      "short note",
      "isolated vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}