{
  "id": "1911.05634",
  "version": "v1",
  "published": "2019-11-13T17:10:42.000Z",
  "updated": "2019-11-13T17:10:42.000Z",
  "title": "Flexible placements of periodic graphs in the plane",
  "authors": [
    "Sean Dewar"
  ],
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "abstract": "Given a periodic graph, we wish to determine via combinatorial methods whether it has perioidic embeddings in the plane that are flexible, i.e. allow motions that preserve edge-lengths and periodicity to non-congruent embeddings. By introducing NBAC-colourings for the corresponding quotient gain graphs, we identify which periodic graphs have flexible embeddings in the plane when the lattice of periodicity is fixed. We further characterise with NBAC-colourings which 1-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity, and characterise in special cases which 2-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-13T17:10:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C25",
      "13A18"
    ],
    "keywords": [
      "periodic graph",
      "flexible placements",
      "flexible embeddings",
      "periodicity",
      "corresponding quotient gain graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}