Extension of paths and cycles for hypergraphs

In [G.Y. Katona and H.A. Kierstead, Hamiltonian chains in hypergraphs, J. Graph Theory (1999) 30(3): 205–212] we defined the hamiltonian cycle in hypergraphs in a new way. The definition can be extended to paths and cycles as well. There are many results for hypergraphs that uses the traditional path and cycle definition of Berge, so almost all of them can be considered with the new definition. In this paper we will deal with such results.