{
  "id": "1808.09245",
  "version": "v1",
  "published": "2018-08-28T12:11:09.000Z",
  "updated": "2018-08-28T12:11:09.000Z",
  "title": "Gallai-Ramsey numbers of odd cycles",
  "authors": [
    "Zhao Wang",
    "Yaping Mao",
    "Colton Magnant",
    "Ingo Sciermeyer",
    "Jinyu Zou"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given two graphs $G$ and $H$ and a positive integer $k$, the $k$-color Gallai-Ramsey number, denoted by $gr_{k}(G : H)$, is the minimum integer $N$ such that for all $n \\geq N$, every $k$-coloring of the edges of $K_{n}$ contains either a rainbow copy of $G$ or a monochromatic copy of $H$. We prove that $gr_{k} (K_{3} : C_{2\\ell + 1}) = \\ell \\cdot 2^{k} + 1$ for all $k \\geq 1$ and $\\ell \\geq 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-28T12:11:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "odd cycles",
      "color gallai-ramsey number",
      "minimum integer",
      "monochromatic copy",
      "rainbow copy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}