{
  "id": "1611.02021",
  "version": "v1",
  "published": "2016-11-07T12:32:53.000Z",
  "updated": "2016-11-07T12:32:53.000Z",
  "title": "Decomposing the vertex set of a hypercube into isomorphic subgraphs",
  "authors": [
    "Vytautas Gruslys"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be an induced subgraph of the hypercube $Q_k$ for some $k$. We show that if $|G|$ is a power of $2$ then, for sufficiciently large $n$, the vertex set of $Q_n$ can be partitioned into induced copies of $G$. This answers a question of Offner. In fact, we prove a stronger statement: if $X$ is a subset of $\\{0,1\\}^k$ for some $k$ and if $|X|$ is a power of $2$, then, for sufficiently large $n$, $\\{0,1\\}^n$ can be partitioned into isometric copies of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-07T12:32:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C51",
      "05B45"
    ],
    "keywords": [
      "vertex set",
      "isomorphic subgraphs",
      "decomposing",
      "isometric copies",
      "stronger statement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}