Exam 4, question 11

W_n consists of a cycle of n vertices with a central vertex connected to all of the vertices of the cycle.

Since n is even, the cycle can be colored with two colors, with the colors alternating around the cycle. Coloring the central vertex with a third color shows that W_n can be colored with 3 colors.

W_n contains three mutually adjacent vertices (the central vertex and two adjacent vertices of the cycle). So W_n cannot be colored with fewer than 3 colors.