{
  "id": "1104.0194",
  "version": "v1",
  "published": "2011-04-01T15:11:00.000Z",
  "updated": "2011-04-01T15:11:00.000Z",
  "title": "Rainbow-free 3-colorings of Abelian Groups",
  "authors": [
    "Amanda Montejano",
    "Oriol Serra"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A 3-coloring of the elements of an abelian group is said to be rainbow--free if there is no 3-term arithmetic progression with its members having pairwise distinct colors. We give a structural characterization of rainbow--free colorings of abelian groups. This characterization proves a conjecture of Jungi\\'c et al. on the size of the smallest chromatic class of a rainbow-free 3-coloring of cyclic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-01T15:11:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10"
    ],
    "keywords": [
      "abelian group",
      "smallest chromatic class",
      "cyclic groups",
      "arithmetic progression",
      "rainbow-free colorings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0194M"
    }
  }
}