{
  "id": "1901.06571",
  "version": "v1",
  "published": "2019-01-19T18:53:43.000Z",
  "updated": "2019-01-19T18:53:43.000Z",
  "title": "Partial cubes with pre-hull number at most 1",
  "authors": [
    "Norbert Polat"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that a connected bipartite graph G is a partial cube if and only if the set of attaching points of any copoint of G is convex. A consequence of this result is that any connected bipartite graph with pre-hull number at most 1 is a partial cube. We show that the class of partial cubes with pre-hull number at most 1 is closed under gated subgraphs, gated amalgams and cartesian products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-19T18:53:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "52A37"
    ],
    "keywords": [
      "partial cube",
      "pre-hull number",
      "connected bipartite graph",
      "cartesian products",
      "attaching points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}