Almost partitioning 2‐colored complete 3‐uniform hypergraphs into two monochromatic tight or loose cycles

We show that for every η > 0 there exists an integer n 0 such that every 2 ‐coloring of the 3 ‐uniform complete hypergraph on n ≥ n 0 vertices contains two disjoint monochromatic tight cycles of distinct colors that together cover all but at most η n vertices. The same result holds if tight cycles are replaced by loose cycles.