Gyárfás's monochromatic tight-cycle partition conjecture

Let $k$ and $r$ be positive integers. A $k$-uniform hypergraph is a hypergraph whose edges are $k$-element subsets of its vertex set, and a tight cycle is a cyclically ordered sequence of vertices in which every $k$ consecutive vertices form an edge; single vertices are also regarded as tight cycles. Gyárfás's conjecture. There is a constant $c=c(k,r)$ such that the vertices of every $r$-edge-coloured complete $k$-uniform hypergraph can be partitioned into at most $c$ monochromatic tight cycles. The paper confirms this conjecture, so the asserted bounded partition exists for all positive integers $k$ and $r$.