  A $h$-sunflower in a hypergraph is a family of edges with $h$ vertices in
common. We show that if we colour the edges of a complete hypergraph in such a
way that any monochromatic $h$-sunflower has at most $\lambda$ petals, then it
contains a large rainbow complete subhypergraph. This extends a theorem by
Lefmann, R\"odl and Wysocka, but this version can be applied to problems in
geometry and algebra. We also give an infinite version of the theorem.

Combinatorics