# Problem property name where an optimal solution in a graph can be used as a solution in any subgraph

Suppose one is given a graph optimization problem where the optimal solution $$S$$ for the problem on graph $$G$$ can be used as a solution for any subgraph of $$G$$. In other words, given $$S$$ is an optimal solution for the problem on $$G$$, then $$S \wedge G_i$$ is a solution on $$G_i$$ all $$G_i \subseteq G$$. Is there a canonical name for this property for a graph optimization problem?

A master solution for an instance of a combinatorial problem is a solution with the property that it is optimal for any sub instance.
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Martijn van Ee, René Sitters:
On the Complexity of Master Problems.
Proceedings of MFCS-2015, LNCS 9235, pp 567-576
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