Edge-disjoint spanners of complete bipartite graphs Original Research Article

A spanning subgraph S=(V,E′) of a connected simple graph G=(V,E) is an (x+c)-spanner if for any pair of vertices u and v, dS(u,v)⩽dG(u,v)+c where dG and dS are the usual distance functions in graphs G and S, respectively. The parameter c is called the delay of the spanner. We investigate the number of edge-disjoint spanners of a given delay that can exist in complete bipartite graphs. We determine the exact number of such edge-disjoint spanners of delay 4 or larger. For delay 2, we obtain many exact values of and some general bounds on this number.