{
  "id": "1912.12542",
  "version": "v1",
  "published": "2019-12-28T23:16:52.000Z",
  "updated": "2019-12-28T23:16:52.000Z",
  "title": "A result on fractional (a,b,k)-critical covered graphs",
  "authors": [
    "Sizhong Zhou",
    "Quanru Pan"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G$, the set of vertices in $G$ is denoted by $V(G)$, and the set of edges in $G$ is denoted by $E(G)$. A fractional $[a,b]$-factor of a graph $G$ is a function $h$ from $E(G)$ to $[0,1]$ satisfying $a\\leq d_G^{h}(v)\\leq b$ for every vertex $v$ of $G$, where $d_G^{h}(v)=\\sum\\limits_{e\\in E(v)}{h(e)}$ and $E(v)=\\{e=uv:u\\in V(G)\\}$. A graph $G$ is called fractional $[a,b]$-covered if $G$ contains a fractional $[a,b]$-factor $h$ with $h(e)=1$ for any edge $e$ of $G$. A graph $G$ is called fractional $(a,b,k)$-critical covered if $G-Q$ is fractional $[a,b]$-covered for any $Q\\subseteq V(G)$ with $|Q|=k$. In this article, we demonstrate a neighborhood condition for a graph to be fractional $(a,b,k)$-critical covered. Furthermore, we claim that the result is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-28T23:16:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70"
    ],
    "keywords": [
      "fractional",
      "covered graphs",
      "neighborhood condition",
      "demonstrate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}