Journal or Book Title
We determine the maximum number of induced copies of a 5-cycle in a graph on n vertices for every n. Every extremal construction is a balanced iterated blow-up of the 5-cycle with the possible exception of the smallest level where for n=8, the Möbius ladder achieves the same number of induced 5-cycles as the blow-up of a 5-cycle on 8 vertices.
This result completes work of Balogh, Hu, Lidický, and Pfender [Eur. J. Comb. 52 (2016)] who proved an asymptotic version of the result. Similarly to their result, we also use the flag algebra method but we extend its use to small graphs.
Lidicky, Bernard; Mattes, Connor; and Pfender, Florian, "C5 is almost a fractalizer" (2021). Mathematics Publications. 265.