Turán numbers of extensions. (English) Zbl 1377.05129
Summary: The extension of an \(r\)-uniform hypergraph \(\mathcal{G}\) is obtained from it by adding for every pair of vertices of \(\mathcal{G}\), which is not covered by an edge in \(\mathcal{G}\), an extra edge containing this pair and \((r - 2)\) new vertices. P. Keevash [in: Surveys in combinatorics 2011. Papers from the 23rd British combinatorial conference, Exeter, UK, July 3–8, 2011. Cambridge: Cambridge University Press. 83–139 (2011; Zbl 1244.05159)] and A. F. Sidorenko [Combinatorica 9, No. 2, 207–215 (1989; Zbl 0732.05031)] have previously determined Turán densities of two families of hypergraph extensions. We determine the Turán numbers for these families, using classical stability techniques and new tools introduced in [S. Norin and L. Yepremyan, J. Comb. Theory, Ser. A 146, 312–343 (2017; Zbl 1351.05163)].
Keywords:
Turán number; extensions; expansions; hypergraphs; stability method; blowup; critical graph; Lagrangian function; covers pairsReferences:
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