Longest cycles in 3-connected hypergraphs and bipartite graphs

Alexandr Kostochka, University of Illinois Urbana-Champaign
Mikhail Lavrov, Kennesaw State University
Ruth Luo, University of California, San Diego
Dara Zirlin, University of Illinois Urbana-Champaign


In the language of hypergraphs, our main result is a Dirac-type bound: We prove that every 3-connected hypergraph (Formula presented.) with (Formula presented.) 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.