Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs IV

Abstract

Finding the values of s for which there exists a maximal set of s edge-disjoint Hamilton cycles in the complete multipartite graph K_n^p 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 s 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).