Partitioning 2-coloured complete k-uniform hypergraphs into monochromatic ℓ-cycles

Abstract

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 kappa((k))(n) 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 & cycles.(C) 2018 Published by Elsevier Ltd.