{
  "id": "1506.07949",
  "version": "v1",
  "published": "2015-06-26T03:22:23.000Z",
  "updated": "2015-06-26T03:22:23.000Z",
  "title": "A sufficient condition for a balanced bipartite digraph to be hamiltonian",
  "authors": [
    "Ruixia Wang"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We describe a new type of sufficient condition for a balanced bipartite digraph to be hamiltonian. Let $D$ be a balanced bipartite digraph and $x,y$ be distinct vertices in $D$. $\\{x, y\\}$ dominates a vertex $z$ if $x\\rightarrow z$ and $y\\rightarrow z$; in this case, we call the pair $\\{x, y\\}$ dominating. In this paper, we prove that a strong balanced bipartite digraph $D$ on $2a$ vertices contains a hamiltonian cycle if, for every dominating pair of vertices $\\{x, y\\}$, either $d(x)\\ge 2a-1$ and $d(y)\\ge a+1$ or $d(x)\\ge a+1$ and $d(y)\\ge 2a-1$. The lower bound in the result is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-26T03:22:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient condition",
      "strong balanced bipartite digraph",
      "distinct vertices",
      "vertices contains",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607949W"
    }
  }
}