Abstract
Let Σ k consist of all k-graphs with three edges D 1, D 2, D 3 such that |D 1 ∩ D 2| = k − 1 and D 1 Δ D 2 ⊆ D 3. The exact value of the Turán function ex(n, Σ k ) was computed for k = 3 by Bollobás [Discrete Math. 8 (1974), 21–24] and for k = 4 by Sidorenko [Math Notes 41 (1987), 247–259].
Let the k-graph T k ∈ Σ k have edges
Frankl and Füredi [J. Combin. Theory Ser. (A) 52 (1989), 129–147] conjectured that there is n 0 = n 0(k) such that ex(n, T k ) = ex(n, Σ k ) for all n ≥ n 0 and had previously proved this for k = 3 in [Combinatorica 3 (1983), 341–349]. Here we settle the case k = 4 of the conjecture.
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Reverts to public domain after 28 years from publication.
Partially supported by the National Science Foundation, Grant DMS-0457512.