Graph coloring is NP-hard so it would be very difficult to replace it with an O(1) algorithm.
If you mean graph coloring restricted to planar graphs, yes it can always be done with at most 4 colors. But it could still be less, so the answer is not always the same.
(I know it was probably not a very serious comment but I just wanted to infodump about graph theory.)
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Graph coloring is NP-hard so it would be very difficult to replace it with an O(1) algorithm.
If you mean graph coloring restricted to planar graphs, yes it can always be done with at most 4 colors. But it could still be less, so the answer is not always the same.
(I know it was probably not a very serious comment but I just wanted to infodump about graph theory.)