Packing 5-cycles into balanced complete m-partite graphs for odd m

Abstract

Let K-n1,(n2),..., n(m) be a complete m-partite graph with partite sets of sizes n(1),n(2),...,n(m). A complete m-partite graph is balanced if each partite set has n vertices. We denote this complete m-partite graph by K-m(n). In this paper, we completely solve the problem of finding a maximum packing of the balanced complete m-partite graph K-m(n), m odd, with edge-disjoint 5-cycles and we explicitly give the minimum leaves.