Please help with this question. Thank you.

A jumping spider lives on a graph G with x[G] = 1:, that is properly colored into k colors. The spider can jump from a vertex to any other vertex of the same color, and also go from any vertex to any vertex connected to it by an edge. Show that the spider can reach any vertex from any other in 3 steps or less. Hint: Show that, in a proper coloring with G] colors, for any pair of colors there is an edge connecting vertices of these two colors