{
  "id": "1412.3497",
  "version": "v1",
  "published": "2014-12-10T23:36:15.000Z",
  "updated": "2014-12-10T23:36:15.000Z",
  "title": "Some existence theorems on all fractional $(g,f)$-factors with prescribed properties",
  "authors": [
    "Sizhong Zhou"
  ],
  "comment": "7pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph, and $g,f:V(G)\\rightarrow Z^{+}$ with $g(x)\\leq f(x)$ for each $x\\in V(G)$. We say that $G$ admits all fractional $(g,f)$-factors if $G$ contains a fractional $r$-factor for every $r:V(G)\\rightarrow Z^{+}$ with $g(x)\\leq r(x)\\leq f(x)$ for any $x\\in V(G)$. Let $H$ be a subgraph of $G$. We say that $G$ has all fractional $(g,f)$-factors excluding $H$ if for every $r:V(G)\\rightarrow Z^{+}$ with $g(x)\\leq r(x)\\leq f(x)$ for all $x\\in V(G)$, $G$ has a fractional $r$-factor $F_h$ such that $E(H)\\cap E(F_h)=\\emptyset$, where $h:E(G)\\rightarrow [0,1]$ is a function. In this paper, we show a characterization for the existence of all fractional $(g,f)$-factors excluding $H$ and obtain two sufficient conditions for a graph to have all fractional $(g,f)$-factors excluding $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-10T23:36:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C72"
    ],
    "keywords": [
      "fractional",
      "existence theorems",
      "prescribed properties",
      "factors excluding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3497Z"
    }
  }
}