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

Abstract

Let r≥k≥2 and Kr×n(k) 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 Kr×n(k) is a partition of the edge set E(Kr×n(k)) into Hamilton cycles. In this paper, we consider the perfect matching decomposition and the tight Hamilton cycle decomposition of Kmk×n(k) for m≥2. We obtain the following results. (1) Let k≥3, m≥1 and n≥1. Then Kmk×n(k) has a perfect matching decomposition. (2) If Kmk(k) has a Hamilton cycle decomposition, then Kmk×n(k) has a tight Hamilton cycle decomposition.