Multicolored parallelisms of Hamiltonian cycles

A subgraph in an edge-colored graph is multicolored   if all its edges receive distinct colors. In this paper, we prove that a complete graph on 2m+12m+1 vertices K2m+1K2m+1 can be properly edge-colored with 2m+12m+1 colors in such a way that the edges of K2m+1K2m+1 can be partitioned into mm multicolored Hamiltonian cycles.