Determine the minimal number of edges a graph G with six vertices must have if [G] is the complete graph 
. If G is Eulerian, then L(G) is Hamiltonian. Does the converse hold? Every chessboard of size m × n (where m ≤ n) admits a knight’s cycle, with the following three exceptions:
(a) m and n are both odd;
(b) m = 1, 2 or 4;
(c) m = 3 and n = 4, 6 or 8.