{
  "id": "1412.3882",
  "version": "v1",
  "published": "2014-12-12T04:03:45.000Z",
  "updated": "2014-12-12T04:03:45.000Z",
  "title": "All fractional (g,f)-factors in graphs",
  "authors": [
    "Zhiren Sun",
    "Sizhong Zhou"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph, and $g,f:V(G)\\rightarrow N$ be two functions with $g(x)\\leq f(x)$ for each vertex $x$ in $G$. We say that $G$ has all fractional $(g,f)$-factors if $G$ includes a fractional $r$-factor for every $r:V(G)\\rightarrow N$ such that $g(x)\\leq r(x)\\leq f(x)$ for each vertex $x$ in $G$. Let $H$ be a subgraph of $G$. We say that $G$ admits all fractional $(g,f)$-factors including $H$ if for every $r:V(G)\\rightarrow N$ with $g(x)\\leq r(x)\\leq f(x)$ for each vertex $x$ in $G$, $G$ includes a fractional $r$-factor $F_h$ with $h(e)=1$ for any $e\\in E(H)$, then we say that $G$ admits all fractional $(g,f)$-factors including $H$, where $h:E(G)\\rightarrow [0,1]$ is the indicator function of $F_h$. In this paper, we obtain a characterization for the existence of all fractional $(g,f)$-factors including $H$ and pose a sufficient condition for a graph to have all fractional $(g,f)$-factors including $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-12T04:03:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70"
    ],
    "keywords": [
      "fractional",
      "sufficient condition",
      "indicator function",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3882S"
    }
  }
}