A subgraph H of an edge-colored graph G is rainbow if all of its edges have different colors. The anti-Ramsey number is the maximum number of colors in an edge-coloring of G with no rainbow copy of H. Originally a complete graph was considered as G. In this paper, we consider a complete bipartite graph as the host graph and discuss some results for the graph H being hamiltonian cycle and perfect matching. Let c (K p , p , t) and m (K p , p , t) be the maximum number of colors in an edge-coloring of the complete bipartite graph K p , p not having t edge-disjoint rainbow hamiltonian cycles and perfect matchings, respectively. We prove that c (K p , p , t) = p 2 - p + t for t ≥ 2 , p ≥ 4 t - 1 and m (K p , p , t) = p 2 - 2 p + t + 1 for t ≥ 2, p ≥ 2 t + 8 . [ABSTRACT FROM AUTHOR]