Let G=(V,E) be a graph, and [math]T \subseteq V[/math]. 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?
This conjecture was formulated by Wu and West . They proved that if T is 10k-edge-connected in G, then G contains k edge-disjoint T-connectors. This has been improved to 6k+6 by DeVos, McDonald, and Pivotto .