{
  "id": "1310.6776",
  "version": "v1",
  "published": "2013-10-24T21:20:13.000Z",
  "updated": "2013-10-24T21:20:13.000Z",
  "title": "Decomposing the cube into paths",
  "authors": [
    "Joshua Erde"
  ],
  "comment": "7 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the question of when the $n$-dimensional hypercube can be decomposed into paths of length $k$. Mollard and Ramras \\cite{MR2013} noted that for odd $n$ it is necessary that $k$ divides $n2^{n-1}$ and that $k\\leq n$. Later, Anick and Ramras \\cite{AR2013} showed that these two conditions are also sufficient for odd $n \\leq 2^{32}$ and conjectured that this was true for all odd $n$. In this note we prove the conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-24T21:20:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decomposing",
      "dimensional hypercube",
      "conjecture",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6776E"
    }
  }
}