Multicolored Spanning Subgraphs in \(G\)-Colorings of Complete Graphs

Abstract

Let \(G = \{g_1, \ldots, g_n\}\) be a finite abelian group. Consider the complete graph \(K_n\) with vertex set \(\{g_1, \ldots, g_n\}\). A \(G\)-coloring of \(K_n\) is a proper edge coloring where the color of edge \(\{g_i, g_j\}\) is \(g_i + g_j\), \(1 \leq i 2\), there exists a proper edge coloring of \(K_p\) which is decomposable into multicolored Hamilton cycles.