{
  "id": "1612.01732",
  "version": "v1",
  "published": "2016-12-06T10:14:23.000Z",
  "updated": "2016-12-06T10:14:23.000Z",
  "title": "Right-angled Artin groups and full subgraphs of graphs",
  "authors": [
    "Takuya Katayama"
  ],
  "comment": "18 pages with 6 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "For a finite graph $\\Gamma$, let $G(\\Gamma)$ be the right-angled Artin group defined by the complement graph of $\\Gamma$. We show that, for any linear forest $\\Lambda$ and any finite graph $\\Gamma$, $G(\\Lambda)$ can be embedded into $G(\\Gamma)$ if and only if $\\Lambda$ can be realised as a full subgraph of $\\Gamma$. We also prove that if we drop the assumption that $\\Lambda$ is a linear forest, then the above assertion does not hold, namely, for any finite graph $\\Lambda$, which is not a linear forest, there exists a finite graph $\\Gamma$ such that $G(\\Lambda)$ can be embedded into $G(\\Gamma)$, though $\\Lambda$ cannot be embedded into $\\Gamma$ as a full subgraph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-06T10:14:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36"
    ],
    "keywords": [
      "right-angled artin group",
      "full subgraph",
      "finite graph",
      "linear forest"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}