Minimizing the number of 5-cycles in graphs with given edge-density

Date
2018-03-01
Authors
Bennett, Patrick
Lidicky, Bernard
Dudek, Andrzej
Lidicky, Bernard
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Mathematics
Organizational Unit
Journal Issue
Series
Department
Mathematics
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.

Comments

This is a manuscript made available through arxiv: https://arxiv.org/abs/1803.00165.

Description
Keywords
Citation
DOI
Source
Collections