{
  "id": "1606.07874",
  "version": "v1",
  "published": "2016-06-25T06:20:56.000Z",
  "updated": "2016-06-25T06:20:56.000Z",
  "title": "On certain hyperplane arrangements and colored graphs",
  "authors": [
    "Joungmin Song"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We exhibit a one-to-one correspondence between $3$-colored graphs and subarrangements of certain hyperplane arrangements denoted $\\mathcal J_n$, $n \\in \\mathbb N$. We define the notion of centrality of $3$-colored graphs which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial $\\chi_{\\mathcal J_n}$ of $\\mathcal J_n$ can be expressed in terms of the number of central $3$-colored graphs, and we compute $\\chi_{\\mathcal J_n}$ for $n = 2, 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-25T06:20:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S22",
      "05C30"
    ],
    "keywords": [
      "colored graphs",
      "hyperplane arrangements",
      "one-to-one correspondence",
      "centrality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}