{
  "id": "1704.01156",
  "version": "v1",
  "published": "2017-04-04T19:16:31.000Z",
  "updated": "2017-04-04T19:16:31.000Z",
  "title": "An explicit edge-coloring of K_n with six colors on every K_5",
  "authors": [
    "Alex Cameron"
  ],
  "comment": "13 pages, 5 figures. arXiv admin note: text overlap with arXiv:1702.06227",
  "categories": [
    "math.CO"
  ],
  "abstract": "For fixed integers p and q, let f(n,p,q) denote the minimum number of colors needed to color all of the edges of the complete graph K_n such that no clique of p vertices spans fewer than q distinct colors. A construction is given which shows that f(n,5,6) < n^(1/2+o(1)). This improves upon the best known probabilistic upper bound of O(n^(3/5)) given by Erd\\H{o}s and Gy\\'arf\\'as. It is also shown that f(n,5,6) = {\\Omega}(n^(1/2)).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-04T19:16:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55",
      "05D10"
    ],
    "keywords": [
      "explicit edge-coloring",
      "probabilistic upper bound",
      "vertices spans fewer",
      "distinct colors",
      "minimum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}