A sunflower anti-Ramsey theorem and its applications
Abstract
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 λ 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.
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