# 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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