Let G be an odd cycle. Prove that any proper 3-coloring of G using the colors red, green, and blue is guaranteed to result in a blue vertex being adjacent to a red and green vertices, a red vertex...

Let G be an odd cycle. Prove that any proper 3-coloring of G using the colors red,
green, and blue is guaranteed to result in a blue vertex being adjacent to a red and
green vertices, a red vertex being adjacent to blue and green vertices, and a green
vertex being adjacent to red and blue vertices