Turan numbers of extensions

摘要

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]. (C) 2017 Published by Elsevier Inc.