Multicolored Isomorphic Spanning Trees in Complete Graphs

Abstract

In this paper, we first prove that if the edges of K-2m are properly colored by 2m - 1 colors in such a way that any two colors induce a 2-factor of which each component is a 4-cycle, then K2m, can be decomposed into m isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2m-1)-edge-colored K-2m for m >= 14.