{
  "id": "2007.04895",
  "version": "v1",
  "published": "2020-07-08T08:32:10.000Z",
  "updated": "2020-07-08T08:32:10.000Z",
  "title": "Asymptotic lower bounds for Gallai-Ramsey functions and numbers",
  "authors": [
    "Zhao Wang",
    "Yaping Mao",
    "Hengzhe Li",
    "Suping Cui"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For two graphs $G,H$ and a positive integer $k$, the \\emph{Gallai-Ramsey number} ${\\rm gr}_k(G,H)$ is defined as the minimum number of vertices $n$ such that any $k$-edge-coloring of $K_n$ contains either a rainbow (all different colored) copy of $G$ or a monochromatic copy of $H$. If $G$ and $H$ are both complete graphs, then we call it \\emph{Gallai-Ramsey function} ${\\rm GR}_k(s,t)$, which is the minimum number of vertices $n$ such that any $k$-edge-coloring of $K_n$ contains either a rainbow copy of $K_s$ or a monochromatic copy of $K_t$. In this paper, we derive some lower bounds for Gallai-Ramsey functions and numbers by Lov\\'{o}sz Local Lemma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-08T08:32:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic lower bounds",
      "gallai-ramsey functions",
      "minimum number",
      "monochromatic copy",
      "local lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}