Let G be a simple graph. G is said to be maximal planar if it is planar and the addition of any new edge to G results in a (simple) non-planar graph....

Let G be a simple graph.  G is said to be maximal planar if it is planar and the addition of any new edge to G results in a (simple) non-planar graph. Examples of maximal non-planar graphs are K4, K5 minus an edge, and K3,3 minus an edge.

(a) Show that a maximal planar graph is connected.

(b) Show that a maximal planar graph of order ≥3 has no bridges.

(c) Show that every face of a maximal planar graph of order ≥3 is bounded by a triangle.