Long Monochromatic Berge Cycles in Colored 4-Uniform Hypergraphs

摘要

Here we prove that for n ≥ 140, in every 3-coloring of the edges of K(4)n there is a monochromatic Berge cycle of length at least n10. This result sharpens an asymptotic result obtained earlier. Another result is that for n ≥ 15, in every 2-coloring of the edges of K(4) n there is a 3-tight Berge cycle of length at least n 10.