{
  "id": "1209.6111",
  "version": "v2",
  "published": "2012-09-27T02:06:55.000Z",
  "updated": "2013-09-03T02:07:35.000Z",
  "title": "On balanced incomplete block designs with specified weak chromatic number",
  "authors": [
    "Daniel Horsley",
    "David A. Pike"
  ],
  "comment": "26 pages, 0 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A weak $c$-colouring of a balanced incomplete block design (BIBD) is a colouring of the points of the design with $c$ colours in such a way that no block of the design has all of its vertices receive the same colour. A BIBD is said to be weakly $c$-chromatic if $c$ is the smallest number of colours with which the design can be weakly coloured. In this paper we show that for all $c \\geq 2$ and $k \\geq 3$ with $(c,k) \\neq (2,3)$, the obvious necessary conditions for the existence of a $(v,k,\\lambda)$-BIBD are asymptotically sufficient for the existence of a weakly $c$-chromatic $(v,k,\\lambda)$-BIBD.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-03T02:07:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05"
    ],
    "keywords": [
      "balanced incomplete block design",
      "specified weak chromatic number",
      "smallest number",
      "obvious necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.6111H"
    }
  }
}