{
  "id": "1703.08261",
  "version": "v1",
  "published": "2017-03-24T01:49:53.000Z",
  "updated": "2017-03-24T01:49:53.000Z",
  "title": "Classification of Book Representations of $K_6$",
  "authors": [
    "Dana Rowland"
  ],
  "comment": "24 pages, 5 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A book representation of a graph is a particular way of embedding a graph in three dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to $K_6$, the complete graph with six vertices. We prove there are exactly 59 distinct book representations for $K_6$, and we identify the number and type of knotted and linked cycles in each representation. We show that book representations of $K_6$ contain between one and seven links, and up to nine knotted cycles. Furthermore, all links and cycles in a book representation of $K_6$ have crossing number at most four.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-24T01:49:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "05C10",
      "57M25"
    ],
    "keywords": [
      "classification",
      "preserves ambient isotopy",
      "distinct book representations",
      "operations",
      "dimensional space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}