{
  "id": "2004.08291",
  "version": "v1",
  "published": "2020-04-17T15:00:12.000Z",
  "updated": "2020-04-17T15:00:12.000Z",
  "title": "Longest cycles in 3-connected hypergraphs and bipartite graphs",
  "authors": [
    "Alexandr Kostochka",
    "Mikhail Lavrov",
    "Ruth Luo",
    "Dara Zirlin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every $3$-connected hypergraph $H$ with $ \\delta(H)\\geq \\max\\{|V(H)|, \\frac{|E(H)|+10}{4}\\}$ has a hamiltonian Berge cycle. This is sharp and refines a conjecture by Jackson from 1981 (in the language of bipartite graphs). Our proofs are in the language of bipartite graphs, since the incidence graph of each hypergraph is bipartite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-17T15:00:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bipartite graphs",
      "longest cycles",
      "hamiltonian berge cycle",
      "dirac-type bound",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}