4-Books of three pages

Let H be a 4-uniform hypergraph on an n-element vertex set V containing no 4-book of 3 pages, i.e., a hypergraph of 4 quadruples with vertices { 1 , 2 , … , 7 } and edges { 1234 , 1235 , 1236 , 4567 } . Then for n > n 0 e ( H ) ⩽ ⌊ n / 2 ⌋ 2 ⌈ n / 2 ⌉ 2 . Moreover, here equality is possible only if V ( H ) can be partitioned into two sets A and B so that each quadruple of H intersects A (and B) in exactly two vertices.