Supersaturation Problem for the Bowtie

@article{Kang2017SupersaturationPF,
  title={Supersaturation Problem for the Bowtie},
  author={Mihyun Kang and Tam{\'a}s Makai and Oleg Pikhurko},
  journal={Electron. Notes Discret. Math.},
  year={2017},
  volume={61},
  pages={679-685}
}
The Tur\'an 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 $q=o(n^2)$. 
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