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Asymptotic solution of the Turán problem for some hypergraphs

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Abstract

Taking an ordinary graphL 2 and replacing each of its vertices by a group ofr/2 vertices (r is even), we get anr-uniform hypergraphL′. In the casex(L 2)=2m+1, we solve asymptotically the Turán problem forL′. Ifx(L 2)#2m+1, the upper bound is still valid but proper constructions are not known.

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Sidorenko, A. Asymptotic solution of the Turán problem for some hypergraphs. Graphs and Combinatorics 8, 199–201 (1992). https://doi.org/10.1007/BF02350635

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