{
  "id": "2011.03929",
  "version": "v1",
  "published": "2020-11-08T09:05:53.000Z",
  "updated": "2020-11-08T09:05:53.000Z",
  "title": "Connectivity keeping paths in $k$-connected bipartite graphs",
  "authors": [
    "Lian Luo",
    "Yingzhi Tian",
    "Liyun Wu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In 2010, Mader [W. Mader, Connectivity keeping paths in $k$-connected graphs, J. Graph Theory 65 (2010) 61-69.] proved that every $k$-connected graph $G$ with minimum degree at least $\\lfloor\\frac{3k}{2}\\rfloor+m-1$ contains a path $P$ of order $m$ such that $G-V(P)$ is still $k$-connected. In this paper, we consider similar problem for bipartite graphs, and prove that every $k$-connected bipartite graph $G$ with minimum degree at least $k+m$ contains a path $P$ of order $m$ such that $G-V(P)$ is still $k$-connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-08T09:05:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "connectivity keeping paths",
      "connected bipartite graph",
      "minimum degree",
      "connected graph",
      "graph theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}