{
  "id": "1511.09277",
  "version": "v1",
  "published": "2015-11-30T12:44:47.000Z",
  "updated": "2015-11-30T12:44:47.000Z",
  "title": "Antifactor of regular bipartite graphs",
  "authors": [
    "Hongliang Lu"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "This problem is NP-complete in general, but for the case when no prescription contains two consecutive gaps, Lov\\'asz gave a structural description, and Cornu\\'ejols gave a polynomial algorithm. However, results on $H$-factors are known only in some special cases, such as parity intervals or general antifactors. Let $k\\geq 3$ be an integer. Let $G'$ be a $k$-regular bipartite graph with partition $(X,Y)$. In this paper, we show that $G'$ contains an $H$-factor, where $H(x)=\\{1\\}$ for all $x\\in X$ and $H(y)=\\{0,2,3,\\ldots,k\\}$ for all $y\\in Y$, which solves a problem proposed by Liu and Yu.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-30T12:44:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regular bipartite graph",
      "cornuejols gave",
      "prescription contains",
      "general antifactors",
      "lovasz gave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151109277L"
    }
  }
}