{
  "id": "1108.5204",
  "version": "v2",
  "published": "2011-08-25T21:24:23.000Z",
  "updated": "2015-11-18T20:41:29.000Z",
  "title": "On anti-Ramsey numbers for complete bipartite graphs and the Turan function",
  "authors": [
    "Elliot Krop",
    "Michelle York"
  ],
  "comment": "4 pages This paper has been withdrawn due to an incomplete argument",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given two graphs $G$ and $H$ with $H\\subseteq G$ we consider the anti-Ramsey function $AR(G,H)$ which is the maximum number of colors in any edge-coloring of $G$ so that every copy of $H$ receives the same color on at least one pair of edges. The classical Tur\\'an function for a graph $G$ and family of graphs $\\mathcal{F}$, written $ex(G,\\mathcal{F})$, is defined as the maximum number of edges of a subgraph of $G$ not containing any member of $\\mathcal{F}$. We show that there exists a constant $c>0$ so that $AR(K_n,K_{s,t})-ex(K_n,K_{s,t})<cn$ and $c$ depends only on $s$ and $t$, which implies $AR(K_n,K_{s,t})\\leq cn^{2-\\frac{1}{s}}$, for $s\\leq t$ by a result of K\\H ovari, S\\'os, and Tur\\'an.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-25T21:24:23.000Z",
      "comment": "4 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-11-18T20:41:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete bipartite graphs",
      "anti-ramsey numbers",
      "maximum number",
      "classical turan function",
      "anti-ramsey function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5204K"
    }
  }
}