Let f (n, r) be the largest integer m with the following property: if the edges of the complete 3-uniform hypergraph Kn3 are colored with r colors then there is a monochromatic component with at least m vertices. Here we show that f (n, 5) ≥ frac(5 n, 7) and f (n, 6) ≥ frac(2 n, 3). Both results are sharp under suitable divisibility conditions (namely if n is divisible by 7, or by 6 respectively).
- Hypergraph edge coloring
- Monochromatic components
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics