{
  "id": "1901.04802",
  "version": "v1",
  "published": "2019-01-15T13:06:27.000Z",
  "updated": "2019-01-15T13:06:27.000Z",
  "title": "Star-critical Ramsey numbers for cycles versus the complete graph on 5 vertices",
  "authors": [
    "Chula J. Jayawardene"
  ],
  "comment": "13 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$, $H$ and $K$ represent three graphs without loops or parallel edges and $n$ represent an integer. Given any red blue coloring of the edges of $G$, we say that $K \\rightarrow (G,H)$, if there exists red copy of $G$ in $K$ or a blue copy of $H$ in $K$. The Ramsey number $r(G, H)$ is defined as $\\min\\{n \\mid K_n\\rightarrow (G,H)\\}$. Likewise, the star-critical Ramsey number $r_*(H, G)$ is defined $\\min\\{k \\mid K_{r(G,H)-1} \\sqcup K_{1,k} \\rightarrow (H, G) \\}$. When $n >6$, in this paper we show that $r_*(C_n,K_5)=3n-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T13:06:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "05C38"
    ],
    "keywords": [
      "star-critical ramsey number",
      "complete graph",
      "parallel edges",
      "blue copy",
      "red copy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}