{
  "id": "1309.4154",
  "version": "v1",
  "published": "2013-09-17T02:18:57.000Z",
  "updated": "2013-09-17T02:18:57.000Z",
  "title": "A neighborhood condition for fractional ID-[a,b]-factor-critical graphs",
  "authors": [
    "Sizhong Zhou",
    "Fan Yang",
    "Zhiren Sun"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph of order $n$, and let $a$ and $b$ be two integers with $1\\leq a\\leq b$. Let $h: E(G)\\rightarrow [0,1]$ be a function. If $a\\leq\\sum_{e\\ni x}h(e)\\leq b$ holds for any $x\\in V(G)$, then we call $G[F_h]$ a fractional $[a,b]$-factor of $G$ with indicator function $h$ where $F_h=\\{e\\in E(G): h(e)>0\\}$. A graph $G$ is fractional independent-set-deletable $[a,b]$-factor-critical (in short, fractional ID-$[a,b]$-factor-critical) if $G-I$ has a fractional $[a,b]$-factor for every independent set $I$ of $G$. In this paper, it is proved that if $n\\geq\\frac{(a+2b)(2a+2b-3)+1}{b}$, $\\delta(G)\\geq\\frac{bn}{a+2b}+a$ and $|N_G(x)\\cup N_G(y)|\\geq\\frac{(a+b)n}{a+2b}$ for any two nonadjacent vertices $x,y\\in V(G)$, then $G$ is fractional ID-$[a,b]$-factor-critical. Furthermore, it is shown that this result is best possible in some sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-17T02:18:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C72",
      "05C35"
    ],
    "keywords": [
      "fractional",
      "neighborhood condition",
      "indicator function",
      "independent set",
      "nonadjacent vertices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4154Z"
    }
  }
}