The maximum number of induced $C_5$'s in a planar graph

Debarun Ghosh, Ervin Győri, Oliver Janzer, Addisu Paulos, Nika Salia, Oscar Zamora

Published 2020-04-02Version 1

Finding the maximum number of induced cycles of length $k$ in a graph on $n$ vertices has been one of the most intriguing open problems of Extremal Graph Theory. Recently Balogh, Hu, Lidick\'{y} and Pfender answered the question in the case $k=5$. In this paper we show that an $n$-vertex planar graph contains at most $\frac{n^2}{3}+O(n)$ induced $C_5$'s, which is asymptotically tight.