Packing $5$-cycles into balanced complete $n$-partite graphs for even $n$: the $1$-factor leave

Abstract

Let $K_{g_1,g_2,\dots ,g_n}$ be a complete $n$-partite graph with partite sets of sizes $g_i$ for $1\le i\le n$. A complete $n$-partite is balanced if each partite set has $g$ vertices. In this paper, we will solve the problem of finding a maximum packing of the balanced complete $n$-partite graph, $n$ even, with edge-disjoint 5-cycles when the leave is a 1-factor.