Campus Units
Mathematics
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
2-24-2021
Journal or Book Title
arXiv
Abstract
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.
Copyright Owner
The Authors
Copyright Date
2021
Language
en
File Format
application/pdf
Recommended Citation
Lidicky, Bernard; Mattes, Connor; and Pfender, Florian, "C5 is almost a fractalizer" (2021). Mathematics Publications. 265.
https://lib.dr.iastate.edu/math_pubs/265
Comments
This preprint is made available through arXiv, https://arxiv.org/abs/2102.06773.