Worst case is : when all components are complete and one component size =n-k+1 since maximum size of a component possible= n-(k-1 )where rest k-1 components are of size 1 and say the components are of m1,m2,....,mk sizes then the set of colors used to color maximum sized components can be used to color the other components too. So in this worst case we will need at least n-k+1 colors so always n-k+1 colorable.
