Improved monochromatic loose cycle partitions in hypergraphs

Improving our earlier result we show that every large enough complete kk-uniform rr-colored hypergraph can be partitioned into at most 50rklog(rk)50rklog(rk) vertex disjoint monochromatic loose cycles. The proof uses a strong hypergraph Regularity Lemma due to Rödl and Schacht and the new, powerful hypergraph Blow-up Lemma of Keevash.