**Problem**Let and be two -uniform hypergraph on the same vertex set . Does there always exist a partition of into classes such that for both , at least hyperedges of meet each of the classes ?

The bound on the number of hyperedges is what one would expect for a random partition. For graphs, the question was answered in the affirmative in [KO]. Keevash and Sudakov observed that the answer is negative if we consider many hypergraphs instead of just 2 (see [KO] for the example).

## Bibliography

*[KO] D. Kühn and D. Osthus, Maximizing several cuts simultaneously, Combinatorics, Probability and Computing 16 (2007), 277-283.

* indicates original appearance(s) of problem.