{
  "id": "1606.03790",
  "version": "v1",
  "published": "2016-06-13T01:57:43.000Z",
  "updated": "2016-06-13T01:57:43.000Z",
  "title": "The super spanning connectivity of arrangement graph",
  "authors": [
    "Pingshan Li",
    "Min Xu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A $k$-container $C(u, v)$ of a graph $G$ is a set of $k$ internally disjoint paths between $u$ and $v$. A $k$-container $C(u, v)$ of $G$ is a $k^*$-container if it is a spanning subgraph of $G$. A graph $G$ is $k^*$-connected if there exists a $k^*$-container between any two different vertices of G. A $k$-regular graph $G$ is super spanning connected if $G$ is $i^*$-container for all $1\\le i\\le k$. In this paper, we prove that the arrangement graph $A_{n, k}$ is super spanning connected if $n\\ge 4$ and $n-k\\ge 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-13T01:57:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "super spanning connectivity",
      "arrangement graph",
      "internally disjoint paths",
      "regular graph",
      "spanning subgraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}