Graph Coloring Problem
It's unclear exactly what level you're asking the question at.

In principle, you could set up a graph where the vertices are prisoners, there's an edge between any two prisoners who need to be kept separate, and each prison corresponds to a colour. In practice, there are probably too many prisoners in any reasonably sized country for this to be a computationally tractable approach (though the conflict graph would probably be rather sparse), there are more constraints on the system that would be hard to model in this graph-colouring approach, and two prisoners getting into a fight could cause a re-colouring that might cause a large proportion of the prison population to be moved, which is neither feasible nor desirable.