
Simultaneous partition of hypergraphs
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.