Let $c < 1$ be some constant and $A_{1}, \dots, A_{m} \subseteq {1, \dots, n}$ be such that $∣ A_{i} ∣ > c n$ for all $i$ and $∣ A_{i} \cap A_{j} ∣ \leq 1$ for all $i \neq = j$ .Must there exist some set $B$ such that $B \cap A_{i} \neq = \emptyset$ and $∣ B \cap A_{i} ∣ ≪_{c} 1$ for all $i$ ?

Worked, still open.

combinatorics · solved · 0 attempts

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