{
  "id": "1710.00118",
  "version": "v1",
  "published": "2017-09-29T23:36:53.000Z",
  "updated": "2017-09-29T23:36:53.000Z",
  "title": "Graphs, Skeleta and Reconstruction of Polytopes",
  "authors": [
    "Margaret M. Bayer"
  ],
  "comment": "16 pages, 1 figure; submitted to Periodica Mathematica Hungarica, special issue in honor of Ted Bisztriczky, Gabor Fejes Toth and Endre Makai",
  "categories": [
    "math.CO"
  ],
  "abstract": "A renowned theorem of Blind and Mani, with a constructive proof by Kalai and an efficiency proof by Friedman, shows that the whole face lattice of a simple polytope can be determined from its graph. This is part of a broader story of reconstructing face lattices from partial information, first considered comprehensively in Gr\\\"unbaum's 1967 book. This survey paper includes varied results and open questions by many researchers on simplicial polytopes, nearly simple polytopes, cubical polytopes, zonotopes, crosspolytopes, and Eulerian posets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-29T23:36:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52-02",
      "52B05",
      "52B12"
    ],
    "keywords": [
      "reconstruction",
      "simple polytope",
      "reconstructing face lattices",
      "broader story",
      "efficiency proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}