# Show that for any graph $G$ there is an ordering of the vertices for which the greedy algorithm requires $χ(G)$ colors.

I'm learning about the greedy algorithm, but this question is to general for me to grasp (I ave no idea where to begin). Could someone please explain how I solve the problem?

Show that for any graph $$G$$ there is an ordering of the vertices for which the greedy algorithm requires $$χ(G)$$ colors.

Start with a coloring with $$\chi(G)$$ colors. Put all the vertices in color class $$1$$ at the start of the ordering. The greedy algorithm with color them all with color $$1$$. Put the vertices in color class $$2$$ next in the ordering. The greedy algorithm will color them all with color $$1$$ or $$2$$. It will not color them all with color $$1$$ though. (Why not?) Continue in this fashion.