1 Prove That The Problem Of Finding A Hamilton Cycle In A Directed Graph Is Np Compl 2538380

1: Prove that the problem of finding a Hamilton cycle in a directed graph is  NP-complete, using the NP-completeness of the Hamilton-cycle problem for undirected graphs.

2. Suppose that two problems are known to be NP-complete. Does this imply that there is a polynomial-time reduction from one to the other, if P INP?