Consider the following version of the Steiner Tree Problem, which we'll refer to as Graphical Steiner Tree. You are given an undirected graph G = (V, E), a set X c V of vertices, and a number k. You want to decide whether there is a set F c E of at most k edges so that in the graph (V, F), X belongs to a single connected component.
Show that Graphical Steiner Tree is NP-complete.
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