Let H be the graph with vertex set Z14 and with edge set

E(H) = {{x, x + 1} : x 2 Z14} [ {{x, x + 5} : x 2 {0, 2, 4, 6, 8, 10, 12}}.

(a) Find the length of a shortest cycle in H and use this to prove that H is non-planar.

(b) Give a different (from part (a)) proof that H is non-planar.