Large sets of wrapped Hamilton cycle decompositions of complete tripartite graphs

Using the Katona-Kierstead definition of a Hamilton cycle in a uniform hypergraph, we settle the existence of wrapped Hamilton cycle decompositions (WHDs) of the λ -fold complete tripartite graph λ K n , n , n with one possible exception. The existence of large sets of WHDs of λ K n , n , n is also settled for all n ? 0 , 1 or 3 ( mod 4 ) .We also investigate the existence of wrapped Hamilton cycle decompositions of the λ -fold complete 3-uniform tripartite hypergraph λ K n , n , n ( 3 ) which have the additional property that they can themselves be partitioned into WHDs (a result reminiscent of partitioning Steiner Quadruple Systems into BIBDs with block size 4).