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Maximal sets of hamilton cycles in complete multipartite graphs

A set S of edge‐disjoint hamilton cycles in a graph G is said to be maximal if the edges in the hamilton cycles in S induce a subgraph H of G such that G − E(H) contains no hamilton cycles. In this context, the spectrum S(G) of a graph G is the set of integers m such that G contains a maximal set of m edge‐disjoint hamilton cycles. This spectrum has previously been determined for all complete graphs and for all complete bipartite graphs. In this paper, we extend these results to the complete multipartite graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 49–66, 2003