Abstract
A family F of k -graphs is called non-principal if its Turán density is strictly smaller than that of each individual member. For each k ⩾ 3 we find two (explicit) k -graphs F and G such that { F , G } is non-principal. Our proofs use stability results for hypergraphs. This completely settles the question posed by Mubayi and Rödl [On the Turán number of triple systems, J. Combin. Theory A, 100 (2002) 135–152]. Also, we observe that the demonstrated non-principality phenomenon holds also with respect to the Ramsey–Turán density as well.
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