Supersaturation problem for the bowtie

M. Kang, T. Makai, O. Pikhurko

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Article number103107
Number of pages27
JournalEuropean Journal of Combinatorics
Publication statusPublished - 2020

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