Terminal-Pairability in Complete Bipartite Graphs

We investigate the terminal-pairibility 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 $\mathrm{\Delta }(D)$ 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.