Rooted topological minors on four vertices

For a graph G and a set Z of four distinct vertices of G, a diamond on Z is a subgraph of G such that, for some labeling Z={v1,v2,v3,v4}, there are three internally disjoint paths P1,P2,P3 with end vertices v1,v2 with v3,v4 on P1,P2, respectively. Therefore, this yields a K4−-subdivision with branch vertices on Z.