2 The vertices of a graph are to be coloured using the following rules:

• all vertices are to be coloured
• no two vertices joined by an edge are to have the same colour.

The following graph has been coloured with four colours.
\includegraphics[max width=\textwidth, alt={}, center]{71ca9c4e-573b-43b7-910d-4bd610af6b27-2_357_883_1683_591} Kempe's rule allows for colours to be swapped. The rule is:

• choose two colours
• draw the subgraph consisting of the vertices coloured with these two colours, together with the edges that connect them
• in any connected part of this subgraph consisting of two or more vertices, the two colours can be swapped.
  1. Use Kempe's rule, choosing the colours blue and red.

Show that the graph can then be coloured with two colours.

Why does Kempe's rule not constitute an algorithm for colouring graphs?