{
  "id": "1311.0137",
  "version": "v1",
  "published": "2013-11-01T10:43:50.000Z",
  "updated": "2013-11-01T10:43:50.000Z",
  "title": "Nearly Planar Graphs and λ-flat Graphs",
  "authors": [
    "Alexander Grigoriev",
    "Athanassios Koutsonas",
    "Dimitrios M. Thilikos"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph G is {\\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\\xi} times. The family of {\\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative parameterized graph family extending the notion of planarity, the {\\lambda}-flat graphs, this time defined as powers of plane graphs in regard to a novel notion of distance, the wall-by-wall distance. We show that the two parameterized graph classes are parametrically equivalent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-01T10:43:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "G.2.2"
    ],
    "keywords": [
      "planar graphs",
      "parameterized graph family extending",
      "plane graphs",
      "novel notion",
      "wall-by-wall distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.0137G"
    }
  }
}