Density of small diameter subgraphs in $K_r$-free graphs

Eng Keat Hng; Domenico Mergoni Cecchelli

Density of small diameter subgraphs in $K_r$-free graphs

Combinatorics 2022-08-01 v1

Authors: Eng Keat Hng , Domenico Mergoni Cecchelli

Abstract

We denote by $\text{ex}(n, H, F)$ the maximum number of copies of $H$ in an $n$ -vertex graph that does not contain $F$ as a subgraph. Recently, Grzesik, Gy\H{o}ri, Salia, Tompkins considered conditions on $H$ under which $\text{ex}(n, H, K_r)$ is asymptotically attained at a blow-up of $K_{r-1}$ , and proposed a conjecture. In this note we disprove their conjecture.

Keywords

extremal graph theory kr-free graphs subgraph density blow-up conjecture disproof

Cite

@article{arxiv.2207.14297,
  title  = {Density of small diameter subgraphs in $K_r$-free graphs},
  author = {Eng Keat Hng and Domenico Mergoni Cecchelli},
  journal= {arXiv preprint arXiv:2207.14297},
  year   = {2022}
}

Comments

3 pages, 2 figures

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