Almost partitioning 2-coloured complete 3-uniform hypergraphs into two monochromatic tight or loose cycles

Abstract

We show that for every {\eta} > 0 there exists an integer n_0 such that every 2-colouring of the 3-uniform complete hypergraph on n \geq n_0 vertices contains two disjoint monochromatic tight cycles of distinct colours that together cover all but at most {\eta}n vertices. The same result holds if we replace tight cycles with loose cycles.