Maximal sets of Hamilton cycles in complete multipartite graphs II

A set S of edge-disjoint hamilton cycles in a graph T is said to be maximal if the hamilton cycles in S form a subgraph of T such that T −E(S) has no hamilton cycle. The set of integers m for which a graph T contains a maximal set of m edge-disjoint hamilton cycles has previously been determined whenever T is a complete graph, a complete bipartite graph, and in many cases when T is a complete multipartite graph. In this paper we solve all but one of the remaining cases when T is a complete multipartite graph. The proof technique could also be used to simplify the proofs of previous results. ∗Department of Mathematics and Statistics, 124-C Wall, Coastal Carolina University, Conway, South Carolina, 29528, USA, [email protected] †Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, Alabama, 36849, USA [email protected]