Two hamiltonian paths P-1 = < u(1),u(2),...,u(n(G))> and P-2 = < v(1), v(2),...,v(n(G))> of G from u to v are independent if u = u(1) = v(1), v = v(n(G)) = u(n(G)), and v(j) not equal u(i) for every 1 < i < n(G). A set of hamiltonian paths, {P-1, P-2,...,
