Terminal-pairability in complete bipartite graphs

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is also bipartite with the same color classes. We improve the lower bound on maximum value of Δ(D) which still guarantees that the demand graph D is terminal-pairable in this setting. We also prove a sharp theorem on the maximum number of edges such a demand graph can have.