The maximum number of induced C5's in a planar graph.

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, Lidický and Pfender answered the question in the case k=5. In this paper we determine precisely, for all sufficiently large n, the maximum number of induced 5‐cycles that an n‐vertex planar graph can contain. [ABSTRACT FROM AUTHOR]