Steiner tree problem for unweighted graphs
[Steiner tree] remains NP-complete if all edge weights are equal, even if $G$&nbsp;is a bipartite graph having no edges joining two vertices in&nbsp;$C$ or two vertices in&nbsp;$V-C$.


&mdash; Garey and Johnson, Computers and Intractability, Freeman, 1979.  Citation is to private communication with E.&nbsp;R. Berlekamp.