# Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs

MacDougall, James A. and Daven, Mike and Rodger, C. A. (2003) Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs. Journal of Graph Theory, 43 . pp. 49-66.

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A set $S$ of edge-disjoint hamilton cycles in a graph $G$ is said to be {\em maximal} if the edges in the hamilton cycles in $S$ induce a subgraph $H$ of $G$ such that $G - EðHÞ contains no hamilton cycles. In this context, the spectrum$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.