Abstract
Finding the values of μ for which there exists a maximal set of μ edge-disjoint Hamilton cycles in the complete multipartite graph Knp has been considered in papers for over 20 years. This paper finally settles the problem by finding such a set in the last remaining open case, namely where μ is as small as possible (so its existence was still in doubt) when n=3 and the number of parts, p, is 3 (mod 4).
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