complexity theory {Hamiltonian, DHC, IND}

Hello,

I need help with a couple of questions.

(The answers haven't come up properly ((Angry)), are too cryptic and I'm having some difficulty).

I'm trying really hard to learn this, so could you explain it as fully and clearly as possible - that would be of great help.

(I find there are some intuitive leaps, or pieces of insight in complexity theory that I don't always see).

a) How do you show that the Hamiltonian Circuit problem is NP-Complete

(do you use gadgets? tsp? I think there is a 'clean' way to do it)

b) If Directed Hamiltonian Circuit is HC but for directed graphs, then how do you show that DHC is NP-Complete

(some how reduce DHC to HC).

2) An **independent set **I is a subset of the nodes of a graph G where: no 2 nodes in I are adjacent in G. *For natural number k, the problem k-IND asks if there is an independent set of size k*. **The problem**: How do you show **k-IND is in Logspace**.

Thank you very much