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 n0 such that every 2-coloring of the 3-uniform complete hypergraph on n ≥ n0 vertices contains two disjoint monochromatic tight cycles of distinct colors that together cover all but at most ηn vertices. The same result holds if tight cycles are replaced by loose cycles. © 2018 Wiley Periodicals Inc.