A Berge-cycle of length k in a hypergraph H is a sequence of distinct vertices and hyperedges v1,h1,v2,h2,…,vk,hk such that vi,vi+1∈hi for all i∈[k], indices taken modulo k. Füredi, Kostochka and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have a Hamiltonian Berge-cycles. We give a sharp Pósa-type lower bound for r-uniform and non-uniform hypergraphs that force Hamiltonian Berge-cycles.
