{
  "id": "math/0202230",
  "version": "v1",
  "published": "2002-02-22T15:13:38.000Z",
  "updated": "2002-02-22T15:13:38.000Z",
  "title": "Equitable coloring of k-uniform hypergraphs",
  "authors": [
    "Raphael Yuster"
  ],
  "comment": "10 Pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $H$ be a $k$-uniform hypergraph with $n$ vertices. A {\\em strong $r$-coloring} is a partition of the vertices into $r$ parts, such that each edge of $H$ intersects each part. A strong $r$-coloring is called {\\em equitable} if the size of each part is $\\lceil n/r \\rceil$ or $\\lfloor n/r \\rfloor$. We prove that for all $a \\geq 1$, if the maximum degree of $H$ satisfies $\\Delta(H) \\leq k^a$ then $H$ has an equitable coloring with $\\frac{k}{a \\ln k}(1-o_k(1))$ parts. In particular, every $k$-uniform hypergraph with maximum degree $O(k)$ has an equitable coloring with $\\frac{k}{\\ln k}(1-o_k(1))$ parts. The result is asymptotically tight. The proof uses a double application of the non-symmetric version of the Lov\\'asz Local Lemma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-22T15:13:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "equitable coloring",
      "k-uniform hypergraphs",
      "maximum degree",
      "lovasz local lemma",
      "non-symmetric version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2230Y"
    }
  }
}