{
  "id": "1301.4583",
  "version": "v1",
  "published": "2013-01-19T18:48:17.000Z",
  "updated": "2013-01-19T18:48:17.000Z",
  "title": "Distinguishing partitions of complete multipartite graphs",
  "authors": [
    "Michael Goff"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A \\textit{distinguishing partition} of a group $X$ with automorphism group ${aut}(X)$ is a partition of $X$ that is fixed by no nontrivial element of ${aut}(X)$. In the event that $X$ is a complete multipartite graph with its automorphism group, the existence of a distinguishing partition is equivalent to the existence of an asymmetric hypergraph with prescribed edge sizes. An asymptotic result is proven on the existence of a distinguishing partition when $X$ is a complete multipartite graph with $m_1$ parts of size $n_1$ and $m_2$ parts of size $n_2$ for small $n_1$, $m_2$ and large $m_1$, $n_2$. A key tool in making the estimate is counting the number of trees of particular classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-19T18:48:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C65",
      "20B25"
    ],
    "keywords": [
      "complete multipartite graph",
      "distinguishing partition",
      "automorphism group",
      "asymmetric hypergraph",
      "nontrivial element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.4583G"
    }
  }
}