Prove that:-
$\bullet$A (open or closed) knight's tour is not possible on a $4\times4$ chess board.
$\bullet$A (open or closed) knight's tour exists on a $8\times8$ chess board.
I want a constructive proof for $8\times8$ board, not just a possible solution. I know that the question boils down to finding a hamiltonian path in Knights' graph.