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It looks like this the paper

Generating all the Steiner trees and computing Steiner intervals for a fixed number of terminals

by Costa Dourado, de Oliveira, and Protti is what you want (available from ScienceDirect). I think the paper gives an algorithm for generating all the minimal (under subgraph inclusion) subgraphs connecting the blue vertices (from which it is easy to obtain all such subgraphs).

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It looks like this paper is what you want. I think the paper gives an algorithm for generating all the minimal (under subgraph inclusion) subgraphs connecting the blue vertices (from which it is easy to obtain all such subgraphs).