Minimizing the number of 5-cycles in graphs with given edge-density Bennett, Patrick Lidicky, Bernard Dudek, Andrzej Lidicky, Bernard
dc.contributor.department Mathematics 2018-10-28T12:27:12.000 2020-06-30T06:00:11Z 2020-06-30T06:00:11Z Mon Jan 01 00:00:00 UTC 2018 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="" target="_blank"></a>.</p>
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dc.identifier.articleid 1184
dc.identifier.contextkey 13167693
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dc.identifier.submissionpath math_pubs/181
dc.language.iso en
dc.source.bitstream archive/|||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
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