Abstract
Let A 1 , A 2 , ..., A m , be at most a and let B 1 , ..., B m , be at most b -element sets and let t be a non-negative integer with the following property | A i ∩ B i | ≤ t and | A i ∩ B i | > t for i ≠ j . Then m ⩽ ( a + b - 2 t a − t ) . The proof uses Lovász's geometrical method and leads to several open problems.
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