Almost partitioning every 2-edge-coloured complete k-graph into k monochromatic tight cycles

Abstract

A $k$-uniform tight cycle is a $k$-graph with a cyclic order of its vertices such that every~$k$ consecutive vertices from an edge. We show that for $k\geq 3$, every red-blue edge-coloured complete $k$-graph on~$n$ vertices contains~$k$ vertex-disjoint monochromatic tight cycles that together cover $n - o(n)$ vertices.