Minimizing the number of 5-cycles in graphs with given edge-density
| dc.contributor.author | Bennett, Patrick | |
| dc.contributor.author | Dudek, Andrzej | |
| dc.contributor.author | Lidicky, Bernard | |
| dc.contributor.author | Pikhurko, Oleg | |
| 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 | 2010-06-05 | |
| dc.description.abstract | <p>Motivated by the work of Razborov about the minimal density of triangles in graphs we study the minimal density of the 5-cycle C5. We show that every graph of order n and size (1−1k)(n2), where k≥3 is an integer, contains at least</p> <p>(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. An SDP solver is not necessary to verify our proofs.</p> | |
| dc.description.comments | <p>This preprint is made available through arxiv: <a href="https://doi.org/10.48550/arXiv.1803.00165" target="_blank"> https://doi.org/10.48550/arXiv.1803.00165</a>.<br/><br/>Published as Bennett P, Dudek A, Lidický B, Pikhurko O. Minimizing the number of 5-cycles in graphs with given edge-density. Combinatorics, Probability and Computing. 2020;29(1):44-67. doi:10.1017/S0963548319000257</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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