Multicolored parallelisms of Hamiltonian cycles

Abstract

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 + 1 vertices K(2m+1) can be properly edge-colored with 2m + 1 colors in such a way that the edges of K(2m+1) can be partitioned into m multicolored Hamiltonian cycles. (C) 2009 Published by Elsevier B.V.