Book free 3-uniform hypergraphs

A k-book in a hypergraph consists of k Berge triangles sharing a common edge. In this paper we prove that the number of the hyperedges in a k-book-free 3-uniform hypergraph on n vertices is at most n28 (1 + o(1)).(c) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by-nc -nd /4 .0/).