{
  "id": "1310.3786",
  "version": "v2",
  "published": "2013-10-14T18:52:22.000Z",
  "updated": "2016-03-31T13:15:38.000Z",
  "title": "On Ramsey numbers of complete graphs with dropped stars",
  "authors": [
    "Jonathan Chappelon",
    "Luis Pedro Montejano",
    "Jorge Ramírez Alfonsín"
  ],
  "comment": "9 pages ; 1 table in Discrete Applied Mathematics, Elsevier, 2016",
  "doi": "10.1016/j.dam.2014.12.005",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $r(G,H)$ be the smallest integer $N$ such that for any $2$-coloring (say, red and blue) of the edges of $K\\_n$, $n\\geqslant N$, there is either a red copy of $G$ or a blue copy of $H$. Let $K\\_n-K\\_{1,s}$ be the complete graph on $n$ vertices from which the edges of $K\\_{1,s}$ are dropped. In this note we present exact values for $r(K\\_m-K\\_{1,1},K\\_n-K\\_{1,s})$ and new upper bounds for $r(K\\_m,K\\_n-K\\_{1,s})$ in numerous cases. We also present some results for the Ramsey number of Wheels versus $K\\_n-K\\_{1,s}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-14T18:52:22.000Z",
      "title": "Upper bounds and values for $r(K_m,K_n-K_{1,s})$ and $r(K_m-e,K_n-K_{1,s})$",
      "abstract": "Let $r(G,H)$ be the smallest integer $N$ such that for any 2-coloring (say, red and blue) of the edges of $K_n$, $n\\ge N$ there is either a red copy of $G$ or a blue copy of $H$. Let $K_n-K_{1,s}$ be the complete graph on $n$ vertices from which the edges of $K_{1,s}$ are dropped. In this note we present exact values for $r(K_m-K_{1,1},K_n-K_{1,s})$ and new upper bounds for $r(K_m,K_n-K_{1,s})$ in numerous cases. We also present some results for the Ramsey number of Wheels versus $K_n-K_{1,s}$.",
      "comment": "9 pages, 1 table",
      "journal": null,
      "doi": null,
      "authors": [
        "Jonathan Chappelon",
        "Luis Pedro Montejano",
        "Jorge Luis Ramírez Alfonsín"
      ]
    },
    {
      "version": "v2",
      "updated": "2016-03-31T13:15:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upper bounds",
      "ramsey number",
      "smallest integer",
      "exact values",
      "complete graph"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3786C"
    }
  }
}