# Edge-disjoint T-connectors

Let G=(V,E) be a graph, and $T \subseteq V$. A T-connector is the union of a family of edge-disjoint paths in G with end-nodes in T, with the property that the end-node pairs of the paths in the family form a connected graph with node set T. Is it true that if T is 3k-edge-connected in G (i.e. there are 3k edge-disjoint paths between any two nodes of T), then G contains k edge-disjoint T-connectors?