On Extremal Hypergraphs for Hamiltonian Cycles

We study sufficient conditions for Hamiltonian cycles in hypergraphs and obtain both Turán- and Dirac-type results. While the Turán-type result gives an exact threshold for the appearance of a Hamiltonian cycle in a hypergraph depending only on the extremal number of a certain path, the Dirac-type result yields just a sufficient condition relying solely on the minimum vertex degree.