Minimizing the number of 5-cycles in graphs with given edge-densityarxiv
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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.
Copyright OwnerThe Authors
Citation InformationPatrick Bennett, Andrzej Dudek and Bernard Lidicky. "Minimizing the number of 5-cycles in graphs with given edge-density" arxiv (2018)
Available at: http://works.bepress.com/bernard-lidicky/49/
This is a manuscript made available through arxiv: https://arxiv.org/abs/1803.00165.