Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

7-8-2020

Journal or Book Title

arXiv

Abstract

The Erdos Pentagon problem asks to find an n-vertex triangle-free graph that is maximizing the number of 5-cycles. The problem was solved using flag algebras by Grzesik and independently by Hatami, Hladky, Kral, Norin, and Razborov. Recently, Palmer suggested the general problem of maximizing the number of 5-cycles in K_{k+1}-free graphs. Using flag algebras, we show that every K_{k+1}-free graph of order n contains at most 110k4(k4−5k3+10k2−10k+4)n5+o(n5)

copies of C_5 for any k≥3, with the Turan graph begin the extremal graph for large enough n.

Comments

This preprint is made available through arXiv: https://arxiv.org/abs/2007.03064.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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