A Fano configuration is the hypergraph of 7 vertices and 7 triplets defined by the points and lines of the finite projective plane of order 2. Proving a conjecture of T. Sós, the largest triple system on n vertices containing no Fano configuration is determined (for n> n₁ ). It is 2-chromatic with n3- n/2 3 - n/2 3 triples. This is one of the very few nontrivial exact results for hypergraph extremal problems.
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Füredi et al. (2005) studied this question.