# Paint graph ordered vertices

I have the following question: Given graph $$G=(V,E)$$ with given order on its vertices, I mean $$v_1 I need to find minimal colors ordered paining of the graph vertices s.t neighbor vertices don’t have the same color, I mean: $$(v_1,v_2,…,v_j)$$ – painted in fist color and non of them are neighbors. $$(v_{j+1},…,v_l)$$ – painted in second color and non of them are neighbors. and so on.

The complexity needs to be $$O(V+E)$$. Anyone have an idea?