Article
Minimizing the number of 5-cycles in graphs with given edge-density
arxiv
Document Type
Article
Disciplines
Publication Version
Submitted Manuscript
Publication Date
3-1-2018
Abstract
Motivated by the work of Razborov about the minimal density of triangles in graphs we study the minimal density of cycles C5. We show that every graph of order n and size (1−1k)(n2), where k≥3 is an integer, contains at least (110−12k+1k2−1k3+25k4)n5+o(n5)
copies of C5. This bound is optimal, since a matching upper bound is given by the balanced complete k-partite graph. The proof is based on the flag algebras framework. We also provide a stability result for 2≤k≤73.
Copyright Owner
The Authors
Copyright Date
2018
Language
en
File Format
application/pdf
Citation Information
Patrick Bennett, Andrzej Dudek and Bernard Lidicky. "Minimizing the number of 5-cycles in graphs with given edge-density" arxiv (2018) Available at: http://works.bepress.com/bernard-lidicky/49/
This is a manuscript made available through arxiv: https://arxiv.org/abs/1803.00165.