Squares of Hamiltonian cycles in 3‐uniform hypergraphs

We show that every 3‐uniform hypergraph H = (V,E) with |V(H)| = n and minimum pair degree at least (4/5 + o(1))n contains a squared Hamiltonian cycle. This may be regarded as a first step towards a hypergraph version of the Pósa‐Seymour conjecture.