Multicolored Spanning Subgraphs in $G$-Colorings of Complete Graphs

Abstract

Let $G=\{g_1,\dots ,g_n\}$ be a finite abelian group. Consider the complete graph $K_n$ with vertex set $\{g_1,\dots ,g_n\}$. A $G$-coloring of $K_n$ is a proper edge coloring where the color of edge $\{g_i,g_j\}$ is $g_i+g_j$, $1\le i2$, there exists a proper edge coloring of $K_p$ which is decomposable into multicolored Hamilton cycles.