If G = (V, E) is an undirected graph, a subset K of V is called a covering of G if for every edge {a, b} of G either a or b is in K. The set K is a minimal covering if K - {x} fails to cover G for each x e K. The number of vertices in a smallest covering is called the covering number of G.
(a) Prove that if I c V, then / is an independent set in G if and only if V - I is a covering of G.
(b) Verify that | V | is the sum of the independence number of G (as defined in Exercise 25 for Section 11.5) and its covering number.