Minimal cover
Task number: 3895
Let \((X, \mathcal P)\) be a finite projective plane of order \(n\). Determine:
Variant
the minimum possible cardinality of a set \( Y \subseteq X \) such that \(\forall P \in \mathcal P: P \cap Y \not= \emptyset\).
Variant
Tightmost bounds on the minimum possible cardinality of a set \(Z \subseteq X\) such that \(\forall P \in \mathcal P: |P\cap Z| \geq 2\).