A “disconnected” graph G ¼ (V, E) can be “divided” into connected “pieces” called components, say G 1 , G 2 , ... Gk, where the vertex set V is partitioned into the vertex sets of the sub graphs, Gj....

A “disconnected” graph G ¼ (V, E) can be “divided” into connected “pieces” called components, say G₁, G₂, ... Gk, where the vertex set V is partitioned into the vertex sets of the sub graphs, Gj. When all the components are trees, G is called a forest. Prove the following:

(a) A graph G is a forest if and only if G has no polygons.

(b) If G is a forest of q trees, then