Labeled K2, t Minors in Plane Graphs

Let G be a 3-connected planar graph and let U⊆V(G). It is shown that G contains a K2, t minor such that t is large and each vertex of degree 2 in K2, t corresponds to some vertex of U if and only if there is no small face cover of U. This result cannot be extended to 2-connected planar graphs.