The perfect matching and tight Hamilton cycle decomposition of complete n-balanced mk-partite k-uniform hypergraphs

Let r > k > 2 and K(k) rxn denote the complete n-balanced r-partite k-uniform hypergraph, whose vertex set consists of r parts, each part has n vertices, and whose edge set contains all the k-element subsets with no two vertices from one part. A Hamilton cycle decomposition of K(k) rxn is a partition of the edge set E(Kr(k)xn) into Hamilton cycles. In this paper, we consider the perfect matching decomposition and the tight Hamilton cycle decomposition of K(k) mkxn for m > 2. We obtain the following results. (1) Let k > 3, m > 1 and n > 1. Then K(k) mkxn has a perfect matching decomposition. (2) If Kmk(k) has a Hamilton cycle decomposition, then K(k) mkxn has a tight Hamilton cycle decomposition. & COPY; 2023 Elsevier B.V. All rights reserved.