Let $K_n^{ (k)}$ be the complete $k$-graph on $n$ vertices. A $k$-uniform tight cycle is a $k$-graph with its vertices cyclically ordered so that every $k$ consecutive vertices form an edge and any two consecutive edges share exactly $k-1$ vertices. A result of Bustamante, Corsten, Frankl, Pokrovskiy and Skokan shows that all $r$-edge coloured $K_{ n}^{ (k)}$ can be partitioned into $c_{ r,k}$ vertex disjoint monochromatic tight cycles. However, the constant $c_{ r,k}$ is of tower-type. In this work, we show that $c_{ r, k}$ is a polynomial in $r$.
Categories: math.CO