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