{
  "id": "2002.00261",
  "version": "v1",
  "published": "2020-02-01T19:21:35.000Z",
  "updated": "2020-02-01T19:21:35.000Z",
  "title": "Excluded minors for the Klein Bottle II. Cascades",
  "authors": [
    "Bojan Mohar",
    "Petr Škoda"
  ],
  "comment": "The original paper arxiv:1406.1341 was split into two parts, this is Part II",
  "categories": [
    "math.CO"
  ],
  "abstract": "Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I, it was shown that graphs that are critical for embeddings into surfaces of Euler genus $k$ or for embeddings into nonorientable surface of genus $k$ are built from 3-connected components, called hoppers and cascades. In Part II, all cascades for Euler genus 2 are classified. As a consequence, the complete list of obstructions of connectivity 2 for embedding graphs into the Klein bottle is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-01T19:21:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "klein bottle",
      "euler genus",
      "minimal excluded minors",
      "complete list",
      "nonorientable surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}