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

dc.contributor.author Bennett, Patrick
dc.contributor.author Lidicky, Bernard
dc.contributor.author Dudek, Andrzej
dc.contributor.author Lidicky, Bernard
dc.contributor.department Mathematics
dc.date 2018-10-28T12:27:12.000
dc.date.accessioned 2020-06-30T06:00:11Z
dc.date.available 2020-06-30T06:00:11Z
dc.date.copyright Mon Jan 01 00:00:00 UTC 2018
dc.date.issued 2018-03-01
dc.description.abstract <p>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)</p> <p>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.</p>
dc.description.comments <p>This is a manuscript made available through arxiv: <a href="https://arxiv.org/abs/1803.00165" target="_blank">https://arxiv.org/abs/1803.00165</a>.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/math_pubs/181/
dc.identifier.articleid 1184
dc.identifier.contextkey 13167693
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/181
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/54570
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/math_pubs/181/2018_Lidicky_MinimizingNumberPreprint.pdf|||Fri Jan 14 21:36:55 UTC 2022
dc.subject.disciplines Discrete Mathematics and Combinatorics
dc.subject.disciplines Mathematics
dc.title Minimizing the number of 5-cycles in graphs with given edge-density
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isAuthorOfPublication a1d8f5ab-9124-4104-981c-8ba1e426e3ff
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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