Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

3-1-2018

Journal or Book Title

arxiv

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.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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