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You can (and people do) do graph coloring on SSA form, just the same as you can do linear scan without SSA. SSA helps graph coloring, in fact, thanks to the discovery that the interference graph of SSA values is chordal and the consequences of that...which was only discovered in 2005.

SSA is more of a control flow representation and is broadly orthogonal to register allocation--you can use graph coloring to allocate registers in SSA and you can do linear scan forms of allocation without SSA.

easier to color graph if you have like 4 registers :-)