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arXiv · 2207.14297

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

Eng Keat Hng·Domenico Mergoni Cecchelli
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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, Győri, 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.

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Eng Keat Hng, Domenico Mergoni Cecchelli. 2022-07-28. Density of small diameter subgraphs in $K_r$-free graphs. https://arxiv.org/abs/2207.14297

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