{
  "id": "2007.02059",
  "version": "v1",
  "published": "2020-07-04T10:01:44.000Z",
  "updated": "2020-07-04T10:01:44.000Z",
  "title": "Gallai-Ramsey numbers for monochromatic $K_4^{+}$ or $K_{3}$",
  "authors": [
    "Xueli Su",
    "Yan Liu"
  ],
  "comment": "18 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Gallai $k$-coloring is a $k$-edge coloring of a complete graph in which there are no rainbow triangles. For two given graphs $H, G$ and two positive integers $k,s$ with that $s\\leq k$, the $k$-colored Gallai-Ramsey number $gr_{k}(K_{3}: s\\cdot H,~ (k-s)\\cdot G)$ is the minimum integer $n$ such that every Gallai $k$-colored $K_{n}$ contains a monochromatic copy of $H$ colored by one of the first $s$ colors or a monochromatic copy of $G$ colored by one of the remaining $k-s$ colors. In this paper, we determine the value of Gallai-Ramsey number in the case that $H=K_{4}^{+}$ and $G=K_{3}$. Thus the Gallai-Ramsey number $gr_{k}(K_{3}: K_{4}^{+})$ is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-04T10:01:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monochromatic copy",
      "rainbow triangles",
      "colored gallai-ramsey number",
      "complete graph",
      "minimum integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}