{
  "id": "2404.05394",
  "version": "v1",
  "published": "2024-04-08T10:53:21.000Z",
  "updated": "2024-04-08T10:53:21.000Z",
  "title": "Spanning plane subgraphs of $1$-plane graphs",
  "authors": [
    "Kenta Noguchi",
    "Katsuhiro Ota",
    "Yusuke Suzuki"
  ],
  "comment": "10 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph drawn on the plane is called $1$-plane if each edge is crossed at most once by another edge. In this paper, we show that every $4$-connected $1$-plane graph has a connected spanning plane subgraph. We also show that there exist infinitely many $4$-connected $1$-plane graphs that have no $2$-connected spanning plane subgraphs. Moreover, we consider the condition of $k$ and $l$ such that every $k$-connected $1$-plane graph has an $l$-connected spanning plane subgraph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-08T10:53:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C10",
      "05C70"
    ],
    "keywords": [
      "plane graph",
      "connected spanning plane subgraph",
      "graph drawn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}