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 \(\forall P \in \mathcal P: |P\cap Z| \geq 2\).

Difficulty level: Moderate task
Reasoning task
Proving or derivation task
Cs translation
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