Tight Contact structures with no Giroux torsion on plumbed 3-manifolds

In this article, we prove a generalization of a theorem of Lisca-Matic to Stein cobordisms. Using this result along with standard techniques from convex surface theory and classifications of tight contact structures on certain 3-manifolds due to Honda, we then classify the contact structures with no Giroux torsion (most of which are Stein fillable) on a certain class of plumbed 3-manifolds that bound non-simply connected 4-manifolds. Moreover, we give descriptions of the Stein fillings.