Corpus ID: 220381400

Maximizing five-cycles in Kr-free graphs

@article{Lidick2020MaximizingFI,
  title={Maximizing five-cycles in Kr-free graphs},
  author={B. Lidick{\'y} and K. Murphy},
  journal={arXiv: Combinatorics},
  year={2020}
}

• B. Lidický, K. Murphy
• Published 2020
• Mathematics
• arXiv: Combinatorics

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 \[\frac{1}{10k^4}(k^4 - 5k^3 + 10k^2 - 10k + 4)n^5 + o(n^5)\] copies of… Expand

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