Turán numbers of extensions

Abstract The extension of an r-uniform hypergraph G is obtained from it by adding for every pair of vertices of G , which is not covered by an edge in G , an extra edge containing this pair and ( r − 2 ) new vertices. Keevash [3] and Sidorenko [9] have previously determined Turan densities of two families of hypergraph extensions. We determine the Turan numbers for these families, using classical stability techniques and new tools introduced in [5] .