Abstract
A family H of isomorphic copies of a given spanning subgraph G is said to be lambda-mutually orthogonal covers (lambda-MOCs) of the complete bipartite graph K-n,K- n by G if every edge of K-n,K- n belongs to exactly lambda members of H and any two different elements from H share at most one edge. In this paper, it is proved that the complete bipartite graph K-p,K- (p), for p prime, has p-MOCs by a path of length p. It is also determined the maximum number M(lambda, n) for which there exist lambda-MOCs of K-n,K- n by all possible subgraphs when n = 3, 4.