The minimum isometric-universal graph for two forests can be computed in polynomial time, while the problem for three forests is NP-complete.
Bodini , On the minimum size of a contraction-universal tree , in 28th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), vol
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Isometric-Universal Graphs for Trees
The minimum isometric-universal graph for two forests can be computed in polynomial time, while the problem for three forests is NP-complete.