Hamiltonian chains in hypergraphs

A cyclic ordering of the vertices of a k-uniform hypergraph is called a hamiltonian chain if any k consecutive vertices in the ordering form an edge. For k = 2 this is the same as a hamiltonian cycle. We consider several natural questions about the new notion. The mam result is a Dirac-type theorem that provide a sufficient condition for finding hamiltonian chains in k-uniforrn hypergraphs with large (k - 1)-minimal degree. If it is more than (1 - 1/2k)n + 4 - k - 5/2k, than the hypergraph contains a hamiltonian chain.