{
  "id": "1611.09096",
  "version": "v1",
  "published": "2016-11-28T12:39:01.000Z",
  "updated": "2016-11-28T12:39:01.000Z",
  "title": "Packing 1-Plane Hamiltonian Cycles in Complete Geometric Graphs",
  "authors": [
    "Hazim Michman Trao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A relaxation for problems in plane geometric graphs is to allow the geometric graphs to be 1-plane. Counting the number of Hamiltonian cycles that are contained in a geometric graph is {\\bf \\#P}-complete even if the graph is known to be planar \\cite{lot:refer}. We consider the problem of backing edge-disjoint 1-plane Hamiltonian cycles in a complete geometric graph $K_{|P|}$ on any set $P$ of $n$ points in general position in the plane. We prove that there are at least $k-1$ sets of 1-plane Hamiltonian cycles that can be packed into $K_{|P|}$, where $n=2^{k}+h$ and $0\\leq h <2^{k}$. We also give bounds for the problem in some special configurations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T12:39:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete geometric graph",
      "hamiltonian cycles",
      "plane geometric graphs",
      "general position",
      "special configurations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}