Thread: Euler & Hamiltonian Circuit proofs

I'm working on these two proofs.
a) I know I need to explain it using 3 cases..
1. When there are no edges
2. When there is 1 common element (1 edge).
3. When there are no common elements (2 edges).

b) I'm thinking in the inductive step, to Let {a1,....an-2} = {1,2,....,n}-{x-y}.
I'm not sure where to go from here..or if I exactly know how to do the basis when n=3.

Any help would be appreciated!

Thanks alot,
Shawn