Which of the following is$/$are True?

I$)$ If PNP$,3-$CLIQUE will be in NP$-$Complete, but not in NP$.$

II$)$ Hamiltonian path problem is in NP$-$Complete, as it is in NP and a NP problem can be reduced to Hamiltonian path problem.

III$)$ Halting problem is NP$-$Complete as well as NP$-$Hard.

IV$)$ Euler's circuit problem is in NP$,$ as it can't be solved in polynomial time.