Multicolored parallelisms of isomorphic spanning trees

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 (m not equal 2) vertices K-2m can be properly edge-colored with 2m - 1 colors in such a way that the edges of K-2m can be partitioned into m multicolored isomorphic spanning trees.