Judicious Partitions of 3-uniform Hypergraphs
A conjecture of Bollobás and Thomason asserts that, for r ≥ 1, every r-uniform hypergraph with m edges can be partitioned into r classes such that every class meets at least rm/(2r - 1) edges. Bollobás, Reed and Thomason  proved that there is a partition in which every edge meets at least (1 - 1/e)m/3 ≈ 0.21m edges. Our main aim is to improve this result for r = 3. We prove that every 3-uniform hypergraph with m edges can be partitioned into three classes, each of which meets at least (5m - 1)/9 edges. We also prove that for r > 3 we may demand 0.27m edges. © 2000 Academic Press.
European Journal of Combinatorics
Bollobás, B., & Scott, A. (2000). Judicious Partitions of 3-uniform Hypergraphs. European Journal of Combinatorics, 21 (3), 289-300. https://doi.org/10.1006/eujc.1998.0266