{
  "id": "1905.03758",
  "version": "v1",
  "published": "2019-05-09T17:15:18.000Z",
  "updated": "2019-05-09T17:15:18.000Z",
  "title": "Super-pancyclic hypergraphs and bipartite graphs",
  "authors": [
    "Alexandr Kostochka",
    "Ruth Luo",
    "Dara Zirlin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We find Dirac-type sufficient conditions for a hypergraph $\\mathcal H$ with few edges to be hamiltonian. We also show that these conditions provide that $\\mathcal H$ is {\\em super-pancyclic}, i.e., for each $A \\subseteq V(\\mathcal H)$ with $|A| \\geq 3$, $\\mathcal H$ contains a Berge cycle with vertex set $A$. We mostly use the language of bipartite graphs, because every bipartite graph is the incidence graph of a multihypergraph. In particular, we extend some results of Jackson on the existence of long cycles in bipartite graphs where the vertices in one part have high minimum degree. Furthermore, we prove a conjecture of Jackson from 1981 on long cycles in 2-connected bipartite graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-09T17:15:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bipartite graph",
      "super-pancyclic hypergraphs",
      "long cycles",
      "dirac-type sufficient conditions",
      "high minimum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}