Longest cycles in 3‐connected hypergraphs and bipartite graphs.

In the language of hypergraphs, our main result is a Dirac‐type bound: We prove that every 3‐connected hypergraph ℋ with δ(H)≥max{∣V(H)∣,∣E(H)∣+ 104} 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. [ABSTRACT FROM AUTHOR]