Supersaturation problem for the bowtie

The Turan function ex(n, F) denotes the maximal number of edges in an F-free graph on n vertices. We consider the function h(F) (n, q), the minimal number of copies of F in a graph on n vertices with ex(n, F) + q edges. The value of h(F) (n, q) has been extensively studied when F is bipartite or colour-critical. In this paper we investigate the simplest remaining graph F, namely, two triangles sharing a vertex, and establish the asymptotic value of h(F) (n, q) for q = o(n(2)). (C) 2020 Elsevier Ltd. All rights reserved.