3. (Kempe Chain Flaw) Suppose that the planar graph G in Figure 1 has been run through a four coloring algorithm using the Kempe chain argument given in class (this was Theorem 3, the flawed proof of Kempe that "showed" that all planar graphs can be four colored). All vertices of G except for v have been magically colored. We are faced with coloring the final vertex v. Try to use Kempe chain switches to color v and explain in detail what goes wrong. RED GREEN GREEN BLUE RED EL BLUE Figure 1: Color v by using Kempe chain switches