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Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.
6
votes
Domination problem with sets
Clearly we can assume that each element in $M$ appears in exactly $4$ subsets. Let $|M| =n$.
Stage 1. Take maximal subfamily $\mathcal{A} \subseteq
\{S_1,....,S_k\} =:\mathcal{S} $ such that:
$\bul …