Combinatorics

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Constructions of non-principal families in extremal hypergraph theory

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

Constructions of Non-Principal Families in Extremal Hypergraph Theory

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} i