{
  "id": "1811.06134",
  "version": "v1",
  "published": "2018-11-15T01:18:29.000Z",
  "updated": "2018-11-15T01:18:29.000Z",
  "title": "Gallai-Ramsey numbers for a class of graphs with five vertices",
  "authors": [
    "Xihe Li",
    "Ligong Wang"
  ],
  "comment": "12 pages,1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given two graphs $G$ and $H$, the $k$-colored Gallai-Ramsey number $gr_k(G : H)$ is defined to be the minimum integer $n$ such that every $k$-coloring of the complete graph on $n$ vertices contains either a rainbow copy of $G$ or a monochromatic copy of $H$. In this paper, we consider $gr_k(K_3 : H)$ where $H$ is a connected graph with five vertices and at most six edges. There are in total thirteen graphs in this graph class, and the Gallai-Ramsey numbers for some of them have been studied step by step in several papers. We determine all the Gallai-Ramsey numbers for the remaining graphs, and we also obtain some related results for a class of unicyclic graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-15T01:18:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C55",
      "05D10"
    ],
    "keywords": [
      "graph class",
      "minimum integer",
      "total thirteen graphs",
      "complete graph",
      "colored gallai-ramsey number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}