{
  "id": "2103.15404",
  "version": "v1",
  "published": "2021-03-29T08:00:46.000Z",
  "updated": "2021-03-29T08:00:46.000Z",
  "title": "Outerspatial 2-complexes: Extending the class of outerplanar graphs to three dimensions",
  "authors": [
    "Johannes Carmesin",
    "Tsvetomir Mihaylov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if and only if it does not contain a surface of positive genus as a subcomplex and does not have a space minor that is a generalised cone over $K_4$ or $K_{2,3}$. This is applied to nested plane embeddings of graphs; that is, plane embeddings constrained by conditions placed on a set of cycles of the graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-29T08:00:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C83",
      "05C10",
      "05E45"
    ],
    "keywords": [
      "outerplanar graphs",
      "outerspatial",
      "dimensions",
      "natural generalisation",
      "o-joung kwon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}