{
  "id": "1111.2413",
  "version": "v1",
  "published": "2011-11-10T08:09:00.000Z",
  "updated": "2011-11-10T08:09:00.000Z",
  "title": "Construction of 2-factors in the middle layer of the discrete cube",
  "authors": [
    "Torsten Mütze",
    "Franziska Weber"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Define the middle layer graph as the graph whose vertex set consists of all bitstrings of length $2n+1$ that have exactly $n$ or $n+1$ entries equal to 1, with an edge between any two vertices for which the corresponding bitstrings differ in exactly one bit. In this work we present an inductive construction of a large family of 2-factors in the middle layer graph for all $n\\geq 1$. We also investigate how the choice of certain parameters used in the construction affects the number and lengths of the cycles in the resulting 2-factor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-10T08:09:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete cube",
      "middle layer graph",
      "vertex set consists",
      "construction affects",
      "entries equal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.2413M"
    }
  }
}