# Edge-disjoint T-connectors

From Egres Open

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?

## Remarks

This conjecture was formulated by Wu and West ^{[1]}. 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 ^{[2]}.

## References

- ↑ D.B. West, H. Wu,
*Packing of Steiner trees and S-connectors in graphs*, DOI link, Author link - ↑ M. DeVos, J. McDonald, I. Pivotto,
*Packing Steiner Trees*, DOI link, arXiv link