Abstract. We prove that if G is a group that splits as a finite graph of finitely generated free groups with cyclic edge groups, and G has no non-Euclidean Baumslag-Solitar subgroups, then G is the fundamental group of a compact nonpositively curved cube complex. In addition, if G is also wordhyperbolic (i.e., if G contains no Baumslag-Solitar subgroups of any type), we show that G is linear (in fact, is a subgroup of SLn(Z)). Contents.