{
  "id": "1809.10298",
  "version": "v1",
  "published": "2018-09-26T17:58:39.000Z",
  "updated": "2018-09-26T17:58:39.000Z",
  "title": "Ramsey and Gallai-Ramsey numbers for two classes of unicyclic graphs",
  "authors": [
    "Zhao Wang",
    "Yaping Mao",
    "Colton Magnant",
    "Jinyu Zou"
  ],
  "comment": "17 pages. arXiv admin note: text overlap with arXiv:1802.04930",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a graph $G$ and a positive integer $k$, define the \\emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $G$. In this paper, we consider two classes of unicyclic graphs, the star with an extra edge and the path with a triangle at one end. We provide the $2$-color Ramsey numbers for these two classes of graphs and use these to obtain general upper and lower bounds on the Gallai-Ramsey numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T17:58:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55"
    ],
    "keywords": [
      "unicyclic graphs",
      "gallai-ramsey numbers",
      "color ramsey numbers",
      "lower bounds",
      "minimum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}