{
  "id": "math/0212373",
  "version": "v1",
  "published": "2002-12-30T06:53:26.000Z",
  "updated": "2002-12-30T06:53:26.000Z",
  "title": "The order of monochromatic subgraphs with a given minimum degree",
  "authors": [
    "Yair Caro",
    "Raphael Yuster"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph. For a given positive integer $d$, let $f_G(d)$ denote the largest integer $t$ such that in every coloring of the edges of $G$ with two colors there is a monochromatic subgraph with minimum degree at least $d$ and order at least $t$. For $n > k > d$ let $f(n,k,d)$ denote the minimum of $f_G(d)$ where $G$ ranges over all graphs with $n$ vertices and minimum degree at least $k$. In this paper we establish $f(n,k,d)$ whenever $k$ or $n-k$ are fixed, and $n$ is sufficiently large. We also consider the case where more than two colors are allowed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-12-30T06:53:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C35"
    ],
    "keywords": [
      "minimum degree",
      "monochromatic subgraph",
      "largest integer",
      "positive integer",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12373C"
    }
  }
}