{
  "id": "0709.2322",
  "version": "v1",
  "published": "2007-09-14T15:16:08.000Z",
  "updated": "2007-09-14T15:16:08.000Z",
  "title": "Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions",
  "authors": [
    "Jesper Lykke Jacobsen"
  ],
  "doi": "10.1088/1751-8113/40/49/003",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-14T15:16:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact enumeration",
      "well-known hamiltonian circuits",
      "square lattices",
      "union visits",
      "hamiltonian chains"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2007,
      "month": "Dec",
      "volume": 40,
      "number": 49,
      "pages": 14667
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JPhA...4014667L"
    }
  }
}