Improved monochromatic loose cycle partitions in hypergraphs

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