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 2 m + 1 vertices K 2 m + 1 can be properly edge-colored with 2 m + 1 colors in such a way that the edges of K 2 m + 1 can be partitioned into m multicolored Hamiltonian cycles.