{
  "id": "1902.10706",
  "version": "v1",
  "published": "2019-02-27T13:18:06.000Z",
  "updated": "2019-02-27T13:18:06.000Z",
  "title": "Gallai-Ramsey numbers for fans",
  "authors": [
    "Yaping Mao",
    "Zhao Wang",
    "Colton Magnant",
    "Ingo Schiermeyer"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1809.10298",
  "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 obtain general upper and lower bounds on the Gallai-Ramsey numbers for fans $F_{m} = K_{1} + mK_{2}$ and prove the sharp result for $m = 2$ and for $m = 3$ with $k$ even.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-27T13:18:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55"
    ],
    "keywords": [
      "gallai-ramsey numbers",
      "minimum number",
      "monochromatic copy",
      "general upper",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}