Partitioning 2-coloured complete [formula omitted]-uniform hypergraphs into monochromatic [formula omitted]-cycles.

We show that for all ℓ , k , n with ℓ ≤ k ∕ 2 and ( k − ℓ ) dividing n the following hypergraph-variant of Lehel’s conjecture is true. Every 2-edge-colouring of the k -uniform complete hypergraph K n ( k ) on n vertices has at most two disjoint monochromatic ℓ -cycles in different colours that together cover all but at most 4 ( k − ℓ ) vertices. If ℓ ≤ k ∕ 3 , then at most two ℓ -cycles cover all but at most 2 ( k − ℓ ) vertices. Furthermore, we can cover all vertices with at most 4 (3 if ℓ ≤ k ∕ 3 ) disjoint monochromatic ℓ -cycles. [ABSTRACT FROM AUTHOR]