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arXiv · 1710.01471

Supersaturation Problem for the Bowtie

Mihyun Kang·Tamás Makai·Oleg Pikhurko
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Abstract

The Turán 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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Mihyun Kang, Tamás Makai, Oleg Pikhurko. 2019-03-26. Supersaturation Problem for the Bowtie. https://arxiv.org/abs/1710.01471

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