For any graph G$,$ does your algorithm always use exactly $\backslash$chi $($G$)$ colours? If so$,$ explain why. If not, provide a graph G for which your algorithm requires more than $\backslash$chi $($G$)$ colours.

Directions $-$ You need to provide a proof of correctness if your algorithm gives the correct chromatic number in all the cases. Otherwise, just a counter example is enough.