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 $K_{ 2m}$ can be decomposed into $m$ isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2$m-$1)-edge-colored $K_{ 2m}$ for $m\geq 14$.
Categories: math.CO