Large sets of wrapped Hamilton cycle decompositions of complete tripartite graphs

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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 λKn,n,n with one possible exception. The existence of large sets of WHDs of λKn,n,n is also settled for all n≡0,1 or 3(mod4).We also investigate the existence of wrapped Hamilton cycle decompositions of the λ-fold complete 3-uniform tripartite hypergraph λKn,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).