Large monochromatic components in colorings of complete 3-uniform hypergraphs

Let f(n,r)f(n,r) be the largest integer mm with the following property: if the edges of the complete 3-uniform hypergraph Kn3 are colored with rr colors then there is a monochromatic component with at least mm vertices. Here we show that f(n,5)≥5n7 and f(n,6)≥2n3. Both results are sharp under suitable divisibility conditions (namely if nn is divisible by 7, or by 6 respectively).