Pósa-type results for Berge-hypergraphs

Abstract

A Berge-cycle of length k in a hypergraph H is a sequence of distinct vertices and hyperedgesindices taken modulo k. Füredi, Kostochka and Luo recently gave sharp Dirac-type minimum degree conditions that force nonuniform 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.